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Mathematical modelling of (re)emerging infectious respiratory diseases among humans poses multiple challenges for modellers, which can arise as a result of limited data and surveillance, uncertainty in the natural history of the disease, as well as public health and individual responses to outbreaks. Here, we propose a COVID-19-inspired health state diagram (HSD) to serve as a foundational framework for conceptualising the modelling process for (re)emerging respiratory diseases, and public health responses, in the early stages of their emergence. The HSD aims to serve as a starting point for reflection on the structure and parameterisation of a transmission model to assess the impact of the (re)emerging disease and the capacity of public health interventions to control transmission. We also explore the adaptability of the HSD to different (re)emerging diseases using the characteristics of three respiratory diseases of historical public health importance. We outline key questions to contemplate when applying and adapting this HSD to (re)emerging infectious diseases and provide reflections on adapting the framework for public health-related interventions., (© 2024. Crown.)

Objectives: Pandemic response in low-income countries (LICs) or settings often suffers from scarce epidemic surveillance and constrained mitigation capacity. The drivers of pandemic burden in such settings, and the impact of limited and delayed interventions remain poorly understood., Methods: We analysed COVID-19 seroprevalence and all-cause excess deaths data from the peri-urban district of Kabwe, Zambia between March 2020 and September 2021 with a novel mathematical model. Data encompassed three consecutive waves caused by the wild-type, Beta and Delta variants., Results: Across all three waves, we estimated a high cumulative attack rate, with 78% (95% credible interval [CrI] 71-85) of the population infected, and a high all-cause excess mortality, at 402 (95% CrI 277-473) deaths per 100,000 people. Ambitiously improving health care to a capacity similar to that in high-income settings could have averted up to 46% (95% CrI 41-53) of accrued excess deaths, if implemented from June 2020 onward. An early and accelerated vaccination rollout could have achieved the highest reductions in deaths. Had vaccination started as in some high-income settings in December 2020 and with the same daily capacity (doses per 100 population), up to 68% (95% CrI 64-71) of accrued excess deaths could have been averted. Slower rollouts would have still averted 62% (95% CrI 58-68), 54% (95% CrI 49-61) or 26% (95% CrI 20-38) of excess deaths if matching the average vaccination capacity of upper-middle-, lower-middle- or LICs, respectively., Conclusions: Robust quantitative analyses of pandemic data are of pressing need to inform future global pandemic preparedness commitments., Competing Interests: Declarations of competing interest The authors have no competing interests to declare., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Background: During the COVID-19 pandemic, the Chinese government implemented nationwide public health interventions to control its spread. However, the impact of these measures on other infectious diseases remains unclear., Methods: The incidence of three types of notifiable infectious diseases in China were analyzed between 2013 and 2021. The seasonal Mann-Kendall test and Mann-Kendall mutation test were employed to examine trends and mutations in the time series. Based on the counterfactual inference, historical incidence rates were employed to construct SARIMA models and predict incidence between January 2020 and December 2021. Differences between reported and predicted incidences during the pandemic were compared using the Mann-Whitney U test., Results: Between 2013 and 2019, the incidence rate of three types of notifiable infectious diseases fluctuated between 494.05/100,000 and 550.62/100,000. No discernible trend was observed for types A and B infectious diseases (Z = -1.344, P = 0.18). A significant upward trend was observed for type C infectious diseases (Z = 2.56, P = 0.01). In 2020, the overall incidence rate of three types of notifiable infectious diseases decreased to 367.08/100,000. Compared to predicted values, the reported incidence of three types of infectious diseases was, on average, 30.05% lower in 2020 and 16.58% lower in 2021., Conclusion: The public health interventions implemented during the pandemic had a positive consequence on the prevention and control of other infectious diseases, with a particularly notable effect on type C infectious diseases. Among the diseases with different transmission routes, respiratory diseases and gastrointestinal or enteroviral diseases decreased significantly., (© 2024. The Author(s).)

Globally, there has been a commitment to produce and distribute a vaccine within 100 days of the next pandemic. This 100-day target will place pressure on countries to make swift decisions on how to optimise vaccine delivery. We used data from the COVID-19 pandemic to inform mathematical modelling of future pandemics in Indonesia for a wide range of pandemic characteristics. We explored the benefits of vaccination programs with different start dates, rollout capacity, and age-specific prioritisation within a year of the detection of a novel pathogen. Early vaccine availability, public uptake of vaccines, and capacity for consistent vaccine delivery were the key factors influencing vaccine benefit. Monitoring age-specific severity will be essential for optimising vaccine benefit. Our study complements existing pathogen-specific pandemic preparedness plans and contributes a tool for the rapid assessment of future threats in Indonesia and similar middle-income countries., Competing Interests: Declaration of competing interest The authors declare that they have no competing financial interests or personal relationships that influenced the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Setting: Mathematical modelling played an important role in the public health response to COVID-19 in Canada. Variability in epidemic trajectories, modelling approaches, and data infrastructure across provinces provides a unique opportunity to understand the factors that shaped modelling strategies., Intervention: Provinces implemented stringent pandemic interventions to mitigate SARS-CoV-2 transmission, considering evidence from epidemic models. This study aimed to summarize provincial COVID-19 modelling efforts. We identified modelling teams working with provincial decision-makers, through referrals and membership in Canadian modelling networks. Information on models, data sources, and knowledge translation were abstracted using standardized instruments., Outcomes: We obtained information from six provinces. For provinces with sustained community transmission, initial modelling efforts focused on projecting epidemic trajectories and healthcare demands, and evaluating impacts of proposed interventions. In provinces with low community transmission, models emphasized quantifying importation risks. Most of the models were compartmental and deterministic, with projection horizons of a few weeks. Models were updated regularly or replaced by new ones, adapting to changing local epidemic dynamics, pathogen characteristics, vaccines, and requests from public health. Surveillance datasets for cases, hospitalizations and deaths, and serological studies were the main data sources for model calibration. Access to data for modelling and the structure for knowledge translation differed markedly between provinces., Implication: Provincial modelling efforts during the COVID-19 pandemic were tailored to local contexts and modulated by available resources. Strengthening Canadian modelling capacity, developing and sustaining collaborations between modellers and governments, and ensuring earlier access to linked and timely surveillance data could help improve pandemic preparedness., (© 2024. The Author(s) under exclusive license to The Canadian Public Health Association.)

Symptom propagation occurs when the symptom set an individual experiences is correlated with the symptom set of the individual who infected them. Symptom propagation may dramatically affect epidemiological outcomes, potentially causing clusters of severe disease. Conversely, it could result in chains of mild infection, generating widespread immunity with minimal cost to public health. Despite accumulating evidence that symptom propagation occurs for many respiratory pathogens, the underlying mechanisms are not well understood. Here, we conducted a scoping literature review for 14 respiratory pathogens to ascertain the extent of evidence for symptom propagation by two mechanisms: dose-severity relationships and route-severity relationships. We identify considerable heterogeneity between pathogens in the relative importance of the two mechanisms, highlighting the importance of pathogen-specific investigations. For almost all pathogens, including influenza and SARS-CoV-2, we found support for at least one of the two mechanisms. For some pathogens, including influenza, we found convincing evidence that both mechanisms contribute to symptom propagation. Furthermore, infectious disease models traditionally do not include symptom propagation. We summarize the present state of modelling advancements to address the methodological gap. We then investigate a simplified disease outbreak scenario, finding that under strong symptom propagation, isolating mildly infected individuals can have negative epidemiological implications.

Wastewater based epidemiology has become a widely used tool for monitoring trends of concentrations of different pathogens, most notably and widespread of SARS-CoV-2. Therefore, in 2022, also in Rhineland-Palatinate, the Ministry of Science and Health has included 16 wastewater treatment sites in a surveillance program providing biweekly samples. However, the mere viral load data is subject to strong fluctuations and has limited value for political deciders on its own. Therefore, the state of Rhineland-Palatinate has commissioned the University Medical Center at Johannes Gutenberg University Mainz to conduct a representative cohort study called SentiSurv, in which an increasing number of up to 12,000 participants have been using sensitive antigen self-tests once or twice a week to test themselves for SARS-CoV-2 and report their status. This puts the state of Rhineland-Palatinate in the fortunate position of having time series of both, the viral load in wastewater and the prevalence of SARS-CoV-2 in the population. Our main contribution is a calibration study based on the data from 2023-01-08 until 2023-10-01 where we identified a scaling factor ( 0.208 ± 0.031 ) and a delay ( 5.07 ± 2.30 days) between the virus load in wastewater, normalized by the pepper mild mottle virus (PMMoV), and the prevalence recorded in the SentiSurv study. The relation is established by fitting an epidemiological model to both time series. We show how that can be used to estimate the prevalence when the cohort data is no longer available and how to use it as a forecasting instrument several weeks ahead of time. We show that the calibration and forecasting quality and the resulting factors depend strongly on how wastewater samples are normalized., (© 2024. The Author(s).)

Background: The international flight network creates multiple routes by which pathogens can quickly spread across the globe. In the early stages of infectious disease outbreaks, analyses using flight passenger data to identify countries at risk of importing the pathogen are common and can help inform disease control efforts. A challenge faced in this modelling is that the latest aviation statistics (referred to as contemporary data) are typically not immediately available. Therefore, flight patterns from a previous year are often used (referred to as historical data). We explored the suitability of historical data for predicting the spatial spread of emerging epidemics., Methods: We analysed monthly flight passenger data from the International Air Transport Association to assess how baseline air travel patterns were affected by outbreaks of Middle East respiratory syndrome (MERS), Zika and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) over the past decade. We then used a stochastic discrete time susceptible-exposed-infected-recovered (SEIR) metapopulation model to simulate the global spread of different pathogens, comparing how epidemic dynamics differed in simulations based on historical and contemporary data., Results: We observed local, short-term disruptions to air travel from South Korea and Brazil for the MERS and Zika outbreaks we studied, whereas global and longer-term flight disruptions occurred during the SARS-CoV-2 pandemic. For outbreak events that were accompanied by local, small and short-term changes in air travel, epidemic models using historical flight data gave similar projections of the timing and locations of disease spread as when using contemporary flight data. However, historical data were less reliable to model the spread of an atypical outbreak such as SARS-CoV-2, in which there were durable and extensive levels of global travel disruption., Conclusion: The use of historical flight data as a proxy in epidemic models is an acceptable practice, except in rare, large epidemics that lead to substantial disruptions to international travel., (© International Society of Travel Medicine 2024. Published by Oxford University Press.)

Background: Defining healthcare facility catchment areas is a key step in predicting future healthcare demand in epidemic settings. Forecasts of hospitalisations can be informed by leading indicators measured at the community level. However, this relies on the definition of so-called catchment areas or the geographies whose populations make up the patients admitted to a given hospital, which are often not well-defined. Little work has been done to quantify the impact of hospital catchment area definitions on healthcare demand forecasting., Methods: We made forecasts of local-level hospital admissions using a scaled convolution of local cases (as defined by the hospital catchment area) and delay distribution. Hospital catchment area definitions were derived from either simple heuristics (in which people are admitted to their nearest hospital or any nearby hospital) or historical admissions data (all emergency or elective admissions in 2019, or COVID-19 admissions), plus a marginal baseline definition based on the distribution of all hospital admissions. We evaluated predictive performance using each hospital catchment area definition using the weighted interval score and considered how this changed by the length of the predictive horizon, the date on which the forecast was made, and by location. We also considered the change, if any, in the relative performance of each definition in retrospective vs. real-time settings, or at different spatial scales., Results: The choice of hospital catchment area definition affected the accuracy of hospital admission forecasts. The definition based on COVID-19 admissions data resulted in the most accurate forecasts at both a 7- and 14-day horizon and was one of the top two best-performing definitions across forecast dates and locations. The "nearby" heuristic also performed well, but less consistently than the COVID-19 data definition. The marginal distribution baseline, which did not include any spatial information, was the lowest-ranked definition. The relative performance of the definitions was larger when using case forecasts compared to future observed cases. All results were consistent across spatial scales of the catchment area definitions., Conclusions: Using catchment area definitions derived from context-specific data can improve local-level hospital admission forecasts. Where context-specific data is not available, using catchment areas defined by carefully chosen heuristics is a sufficiently good substitute. There is clear value in understanding what drives local admissions patterns, and further research is needed to understand the impact of different catchment area definitions on forecast performance where case trends are more heterogeneous., (© 2024. The Author(s).)

Background: Since the emergence of SARS-CoV-2 (COVID-19), there have been multiple waves of infection and multiple rounds of vaccination rollouts. Both prior infection and vaccination can prevent future infection and reduce severity of outcomes, combining to form hybrid immunity against COVID-19 at the individual and population level. Here, we explore how different combinations of hybrid immunity affect the size and severity of near-future Omicron waves., Methods: To investigate the role of hybrid immunity, we use an agent-based model of COVID-19 transmission with waning immunity to simulate outbreaks in populations with varied past attack rates and past vaccine coverages, basing the demographics and past histories on the World Health Organization Western Pacific Region., Results: We find that if the past infection immunity is high but vaccination levels are low, then the secondary outbreak with the same variant can occur within a few months after the first outbreak; meanwhile, high vaccination levels can suppress near-term outbreaks and delay the second wave. Additionally, hybrid immunity has limited impact on future COVID-19 waves with immune-escape variants., Conclusions: Enhanced understanding of the interplay between infection and vaccine exposure can aid anticipation of future epidemic activity due to current and emergent variants, including the likely impact of responsive vaccine interventions., (© 2024. The Author(s).)

Background: Highlighted by the rise of COVID-19, climate change, and conflict, socially vulnerable populations are least resilient to disaster. In infectious disease management, mathematical models are a commonly used tool. Researchers should include social vulnerability in models to strengthen their utility in reflecting real-world dynamics. We conducted a scoping review to evaluate how researchers have incorporated social vulnerability into infectious disease mathematical models., Methods: The methodology followed the Joanna Briggs Institute and updated Arksey and O'Malley frameworks, verified by the PRISMA-ScR checklist. PubMed, Clarivate Web of Science, Scopus, EBSCO Africa Wide Information, and Cochrane Library were systematically searched for peer-reviewed published articles. Screening and extracting data were done by two independent researchers., Results: Of 4075 results, 89 articles were identified. Two-thirds of articles used a compartmental model (n = 58, 65.2%), with a quarter using agent-based models (n = 24, 27.0%). Overall, routine indicators, namely age and sex, were among the most frequently used measures (n = 42, 12.3%; n = 22, 6.4%, respectively). Only one measure related to culture and social behaviour (0.3%). For compartmental models, researchers commonly constructed distinct models for each level of a social vulnerability measure and included new parameters or influenced standard parameters in model equations (n = 30, 51.7%). For all agent-based models, characteristics were assigned to hosts (n = 24, 100.0%), with most models including age, contact behaviour, and/or sex (n = 18, 75.0%; n = 14, 53.3%; n = 10, 41.7%, respectively)., Conclusions: Given the importance of equitable and effective infectious disease management, there is potential to further the field. Our findings demonstrate that social vulnerability is not considered holistically. There is a focus on incorporating routine demographic indicators but important cultural and social behaviours that impact health outcomes are excluded. It is crucial to develop models that foreground social vulnerability to not only design more equitable interventions, but also to develop more effective infectious disease control and elimination strategies. Furthermore, this study revealed the lack of transparency around data sources, inconsistent reporting, lack of collaboration with local experts, and limited studies focused on modelling cultural indicators. These challenges are priorities for future research., (© 2024. The Author(s).)

Objectives: The amount of SARS-CoV-2 detected in the upper respiratory tract (URT viral load) is a key driver of transmission of infection. Current evidence suggests that mechanisms constraining URT viral load are different from those controlling lower respiratory tract viral load and disease severity. Understanding such mechanisms may help to develop treatments and vaccine strategies to reduce transmission. Combining mathematical modelling of URT viral load dynamics with transcriptome analyses we aimed to identify mechanisms controlling URT viral load., Methods: COVID-19 patients were recruited in Spain during the first wave of the pandemic. RNA sequencing of peripheral blood and targeted NanoString nCounter transcriptome analysis of nasal epithelium were performed and gene expression analysed in relation to paired URT viral load samples collected within 15 days of symptom onset. Proportions of major immune cells in blood were estimated from transcriptional data using computational differential estimation. Weighted correlation network analysis (adjusted for cell proportions) and fixed transcriptional repertoire analysis were used to identify associations with URT viral load, quantified as standard deviations (z-scores) from an expected trajectory over time., Results: Eighty-two subjects (50% female, median age 54 years (range 3-73)) with COVID-19 were recruited. Paired URT viral load samples were available for 16 blood transcriptome samples, and 17 respiratory epithelial transcriptome samples. Natural Killer (NK) cells were the only blood cell type significantly correlated with URT viral load z-scores (r = -0.62, P = 0.010). Twenty-four blood gene expression modules were significantly correlated with URT viral load z-score, the most significant being a module of genes connected around IFNA14 (Interferon Alpha-14) expression (r = -0.60, P = 1e-10). In fixed repertoire analysis, prostanoid-related gene expression was significantly associated with higher viral load. In nasal epithelium, only GNLY (granulysin) gene expression showed significant negative correlation with viral load., Conclusions: Correlations between the transcriptional host response and inter-individual variations in SARS-CoV-2 URT viral load, revealed many molecular mechanisms plausibly favouring or constraining viral replication. Existing evidence corroborates many of these mechanisms, including likely roles for NK cells, granulysin, prostanoids and interferon alpha-14. Inhibition of prostanoid production and administration of interferon alpha-14 may be attractive transmission-blocking interventions., Competing Interests: Declaration of Competing Interest The authors declare that they have no competing interests., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Background: Italy has a high HCV prevalence, and despite the approval of a dedicated fund for 'Experimental screening' for 2 years, screening has not been fully implemented. We aimed to evaluate the long-term impact of the persisting delay in HCV elimination after the Coronavirus disease 2019 (COVID-19) pandemic in Italy., Methods: We used a mathematical, probabilistic modelling approach evaluating three hypothetical 'Inefficient', 'Efficient experimental' and 'WHO Target' screening scenarios differing by treatment rates over time. A Markov chain for liver disease progression evaluated the number of active infections, decompensated cirrhosis (DC), hepatocellular carcinoma (HCC) and HCV liver-related deaths up to the years 2030 and 2050., Results: The 'WHO Target' scenario estimated 3900 patients with DC and 600 with HCC versus 4400 and 600 cases, respectively, similar for both 'Inefficient' and 'Efficient experimental' screening up to 2030. A sharp (10-fold) decrease in DC and HCC was estimated by the 'WHO Target' scenario compared with the other two scenarios in 2050; the forecasted number of DC was 420 cases versus 4200 and 3800 and of HCC <10 versus 600 and 400 HCC cases by 'WHO Target,' 'Inefficient' and 'Efficient experimental' scenarios, respectively. A significant decrease of the cumulative estimated number of liver-related deaths was observed up to 2050 by the 'WHO Target' scenario (52000) versus 'Inefficient' or 'Efficient experimental' scenarios (79 000 and 74 000 liver-related deaths, respectively)., Conclusions: Our estimates highlight the need to extensively and efficiently address HCV screening and cure of HCV infection in order to avoid the forecasted long-term HCV adverse outcomes in Italy., (© 2023 The Authors. Liver International published by John Wiley & Sons Ltd.)

The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

The evolution of SARS-CoV-2 has demonstrated that emerging variants can set back the global COVID-19 response. The ability to rapidly assess the threat of new variants is critical for timely optimisation of control strategies. We present a novel method to estimate the effective transmission advantage of a new variant compared to a reference variant combining information across multiple locations and over time. Through an extensive simulation study designed to mimic real-time epidemic contexts, we show that our method performs well across a range of scenarios and provide guidance on its optimal use and interpretation of results. We also provide an open-source software implementation of our method. The computational speed of our tool enables users to rapidly explore spatial and temporal variations in the estimated transmission advantage. We estimate that the SARS-CoV-2 Alpha variant is 1.46 (95% Credible Interval 1.44-1.47) and 1.29 (95% CrI 1.29-1.30) times more transmissible than the wild type, using data from England and France respectively. We further estimate that Delta is 1.77 (95% CrI 1.69-1.85) times more transmissible than Alpha (England data). Our approach can be used as an important first step towards quantifying the threat of emerging or co-circulating variants of infectious pathogens in real-time., Competing Interests: Declaration of Competing Interest AC has received payment from Pfizer for teaching of mathematical modelling of infectious diseases., (Copyright © 2023 The Author(s). Published by Elsevier B.V. All rights reserved.)

Background: Respiratory syncytial virus (RSV) is a leading cause of hospitalisation and mortality in young children globally. The social distancing measures implemented against COVID-19 in Lombardy (Italy) disrupted the typically seasonal RSV circulation during 2019-2021 and caused substantially more hospitalisations during 2021-2022. The primary aim of this study is to quantify the immunity gap-defined as the increased proportion of the population naïve to RSV infection following the relaxation of COVID-19 restrictions in Lombardy, which has been hypothesised to be a potential cause of the increased RSV burden in 2021-2022., Methods: We developed a catalytic model to reconstruct changes in the age-dependent susceptibility profile of the Lombardy population throughout the COVID-19 pandemic. The model is calibrated to routinely collected hospitalisation, syndromic, and virological surveillance data and tested for alternative assumptions on age-dependencies in the risk of RSV infection throughout the pandemic., Findings: We estimate that the proportion of the Lombardy population naïve to RSV infection increased by 60.8% (95% CrI: 55.2-65.4%) during the COVID-19 pandemic: from 1.4% (95% CrI: 1.3-1.6%) in 2018-2019 to 2.3% (95% CrI: 2.2-2.5%) before the 2021-2022 season, corresponding to an immunity gap of 0.87% (95% CrI: 0.87-0.88%). We found evidence of heterogeneity in RSV transmission by age, suggesting that the COVID-19 restrictions had variable impact on the contact patterns and risk of RSV infection across ages., Interpretation: We estimate a substantial increase in the population-level susceptibility to RSV in Lombardy during 2019-2021, which contributed to an increase in primary RSV infections in 2021-2022., Funding: UK Medical Research Council (MRC), UK Foreign, Commonwealth & Development Office (FCDO), EDCTP2 programme, European Union, Wellcome Trust, Royal Society, EU-MUR PNRR INF-ACT., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

Objectives: Clustering pathogen sequence data is a common practice in epidemiology to gain insights into the genetic diversity and evolutionary relationships among pathogens. We can find groups of cases with a shared transmission history and common origin, as well as identifying transmission hotspots. Motivated by the experience of clustering SARS-CoV-2 cases using whole genome sequence data during the COVID-19 pandemic to aid with public health investigation, we investigated how differences in epidemiology and sampling can influence the composition of clusters that are identified., Methods: We performed genomic clustering on simulated SARS-CoV-2 outbreaks produced with different transmission rates and levels of genomic diversity, along with varying the proportion of cases sampled., Results: In single outbreaks with a low transmission rate, decreasing the sampling fraction resulted in multiple, separate clusters being identified where intermediate cases in transmission chains are missed. Outbreaks simulated with a high transmission rate were more robust to changes in the sampling fraction and largely resulted in a single cluster that included all sampled outbreak cases. When considering multiple outbreaks in a sampled jurisdiction seeded by different introductions, low genomic diversity between introduced cases caused outbreaks to be merged into large clusters. If the transmission and sampling fraction, and diversity between introductions was low, a combination of the spurious break-up of outbreaks and the linking of closely related cases in different outbreaks resulted in clusters that may appear informative, but these did not reflect the true underlying population structure. Conversely, genomic clusters matched the true population structure when there was relatively high diversity between introductions and a high transmission rate., Conclusion: Differences in epidemiology and sampling can impact our ability to identify genomic clusters that describe the underlying population structure. These findings can help to guide recommendations for the use of pathogen clustering in public health investigations., Competing Interests: Declaration of Competing Interest The authors declare they have no competing interests., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

Since the emergence of SARS-CoV-2 in 2019 through to mid-2021, much of the Australian population lived in a COVID-19-free environment. This followed the broadly successful implementation of a strong suppression strategy, including international border closures. With the availability of COVID-19 vaccines in early 2021, the national government sought to transition from a state of minimal incidence and strong suppression activities to one of high vaccine coverage and reduced restrictions but with still-manageable transmission. This transition is articulated in the national 're-opening' plan released in July 2021. Here, we report on the dynamic modelling study that directly informed policies within the national re-opening plan including the identification of priority age groups for vaccination, target vaccine coverage thresholds and the anticipated requirements for continued public health measures-assuming circulation of the Delta SARS-CoV-2 variant. Our findings demonstrated that adult vaccine coverage needed to be at least 60% to minimize public health and clinical impacts following the establishment of community transmission. They also supported the need for continued application of test-trace-isolate-quarantine and social measures during the vaccine roll-out phase and beyond.

Background: Long-lasting nonpharmaceutical interventions (NPIs) suppressed the infection of COVID-19 but came at a substantial economic cost and the elevated risk of the outbreak of respiratory infectious diseases (RIDs) following the pandemic. Policymakers need data-driven evidence to guide the relaxation with adaptive NPIs that consider the risk of both COVID-19 and other RIDs outbreaks, as well as the available healthcare resources., Methods: Combining the COVID-19 data of the sixth wave in Hong Kong between May 31, 2022 and August 28, 2022, 6-year epidemic data of other RIDs (2014-2019), and the healthcare resources data, we constructed compartment models to predict the epidemic curves of RIDs after the COVID-19-targeted NPIs. A deep reinforcement learning (DRL) model was developed to learn the optimal adaptive NPIs strategies to mitigate the outbreak of RIDs after COVID-19-targeted NPIs are lifted with minimal health and economic cost. The performance was validated by simulations of 1000 days starting August 29, 2022. We also extended the model to Beijing context., Findings: Without any NPIs, Hong Kong experienced a major COVID-19 resurgence far exceeding the hospital bed capacity. Simulation results showed that the proposed DRL-based adaptive NPIs successfully suppressed the outbreak of COVID-19 and other RIDs to lower than capacity. DRL carefully controlled the epidemic curve to be close to the full capacity so that herd immunity can be reached in a relatively short period with minimal cost. DRL derived more stringent adaptive NPIs in Beijing., Interpretation: DRL is a feasible method to identify the optimal adaptive NPIs that lead to minimal health and economic cost by facilitating gradual herd immunity of COVID-19 and mitigating the other RIDs outbreaks without overwhelming the hospitals. The insights can be extended to other countries/regions., (© The Author(s) 2023. Published by Oxford University Press on behalf of the American Medical Informatics Association. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries., (© 2023. The Author(s).)

Background: During the early stages of the COVID-19 pandemic, there was considerable uncertainty surrounding epidemiological and clinical aspects of SARS-CoV-2. Governments around the world, starting from varying levels of pandemic preparedness, needed to make decisions about how to respond to SARS-CoV-2 with only limited information about transmission rates, disease severity and the likely effectiveness of public health interventions. In the face of such uncertainties, formal approaches to quantifying the value of information can help decision makers to prioritise research efforts., Methods: In this study we use Value of Information (VoI) analysis to quantify the likely benefit associated with reducing three key uncertainties present in the early stages of the COVID-19 pandemic: the basic reproduction number ([Formula: see text]), case severity (CS), and the relative infectiousness of children compared to adults (CI). The specific decision problem we consider is the optimal level of investment in intensive care unit (ICU) beds. Our analysis incorporates mathematical models of disease transmission and clinical pathways in order to estimate ICU demand and disease outcomes across a range of scenarios., Results: We found that VoI analysis enabled us to estimate the relative benefit of resolving different uncertainties about epidemiological and clinical aspects of SARS-CoV-2. Given the initial beliefs of an expert, obtaining more information about case severity had the highest parameter value of information, followed by the basic reproduction number [Formula: see text]. Resolving uncertainty about the relative infectiousness of children did not affect the decision about the number of ICU beds to be purchased for any COVID-19 outbreak scenarios defined by these three parameters., Conclusion: For the scenarios where the value of information was high enough to justify monitoring, if CS and [Formula: see text] are known, management actions will not change when we learn about child infectiousness. VoI is an important tool for understanding the importance of each disease factor during outbreak preparedness and can help to prioritise the allocation of resources for relevant information., (© 2023. Crown.)

Background: To reduce the burden from the COVID-19 pandemic in the United States, federal and state local governments implemented restrictions such as limitations on gatherings, restaurant dining, and travel, and recommended non-pharmaceutical interventions including physical distancing, mask-wearing, surface disinfection, and increased hand hygiene. Resulting behavioral changes impacted other infectious diseases including enteropathogens such as norovirus and rotavirus, which had fairly regular seasonal patterns prior to the COVID-19 pandemic. The study objective was to project future incidence of norovirus and rotavirus gastroenteritis as contacts resumed and other NPIs are relaxed., Methods: We fitted compartmental mathematical models to pre-pandemic U.S. surveillance data (2012-2019) for norovirus and rotavirus using maximum likelihood estimation. Then, we projected incidence for 2022-2030 under scenarios where the number of contacts a person has per day varies from70%, 80%, 90%, and full resumption (100%) of pre-pandemic levels., Results: We found that the population susceptibility to both viruses increased between March 2020 and November 2021. The 70-90% contact resumption scenarios led to lower incidence than observed pre-pandemic for both viruses. However, we found a greater than two-fold increase in community incidence relative to the pre-pandemic period under the 100% contact scenarios for both viruses. With rotavirus, for which population immunity is driven partially by vaccination, patterns settled into a new steady state quickly in 2022 under the 70-90% scenarios. For norovirus, for which immunity is relatively short-lasting and only acquired through infection, surged under the 100% contact scenario projection., Conclusions: These results, which quantify the consequences of population susceptibility build-up, can help public health agencies prepare for potential resurgence of enteric viruses., (© 2023. The Author(s).)

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics"., Competing Interests: Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Background: Understanding the overall effectiveness of non-pharmaceutical interventions to control the COVID-19 pandemic and reduce the burden of disease is crucial for future pandemic planning. However, quantifying the effectiveness of specific control measures and the extent of missed infections, in the absence of early large-scale serological surveys or random community testing, has remained challenging., Methods: Combining data on notified local COVID-19 cases with known and unknown sources of infections in Singapore with a branching process model, we reconstructed the incidence of missed infections during the early phase of the wild-type SARS-CoV-2 and Delta variant transmission. We then estimated the relative effectiveness of border control measures, case finding and contact tracing when there was no or low vaccine coverage in the population. We compared the risk of ICU admission and death between the wild-type SARS-CoV-2 and the Delta variant in notified cases and all infections., Results: We estimated strict border control measures were associated with 0.2 (95% credible intervals, CrI 0.04-0.8) missed imported infections per notified case between July and December 2020, a decline from around 1 missed imported infection per notified case in the early phases of the pandemic. Contact tracing was estimated to identify 78% (95% CrI 62-93%) of the secondary infections generated by notified cases before the partial lockdown in Apr 2020, but this declined to 63% (95% CrI 56-71%) during the lockdown and rebounded to 78% (95% CrI 58-94%) during reopening in Jul 2020. The contribution of contact tracing towards overall outbreak control also hinges on ability to find cases with unknown sources of infection: 42% (95% CrI 12-84%) of such cases were found prior to the lockdown; 10% (95% CrI 7-15%) during the lockdown; 47% (95% CrI 17-85%) during reopening, due to increased testing capacity and health-seeking behaviour. We estimated around 63% (95% CrI 49-78%) of the wild-type SARS-CoV-2 infections were undetected during 2020 and around 70% (95% CrI 49-91%) for the Delta variant in 2021., Conclusions: Combining models with case linkage data enables evaluation of the effectiveness of different components of outbreak control measures, and provides more reliable situational awareness when some cases are missed. Using such approaches for early identification of the weakest link in containment efforts could help policy makers to better redirect limited resources to strengthen outbreak control., (© 2023. The Author(s).)

Introduction: In 2016, South Africa (SA) initiated a national programme to scale-up pre-exposure prophylaxis (PrEP) among female sex workers (FSWs), with ∼20,000 PrEP initiations among FSWs (∼14% of FSW) by 2020. We evaluated the impact and cost-effectiveness of this programme, including future scale-up scenarios and the potential detrimental impact of the COVID-19 pandemic., Methods: A compartmental HIV transmission model for SA was adapted to include PrEP. Using estimates on self-reported PrEP adherence from a national study of FSW (67.7%) and the Treatment and Prevention for FSWs (TAPS) PrEP demonstration study in SA (80.8%), we down-adjusted TAPS estimates for the proportion of FSWs with detectable drug levels (adjusted range: 38.0-70.4%). The model stratified FSW by low (undetectable drug; 0% efficacy) and high adherence (detectable drug; 79.9%; 95% CI: 67.2-87.6% efficacy). FSWs can transition between adherence levels, with lower loss-to-follow-up among highly adherent FSWs (aHR: 0.58; 95% CI: 0.40-0.85; TAPS data). The model was calibrated to monthly data on the national scale-up of PrEP among FSWs over 2016-2020, including reductions in PrEP initiations during 2020. The model projected the impact of the current programme (2016-2020) and the future impact (2021-2040) at current coverage or if initiation and/or retention are doubled. Using published cost data, we assessed the cost-effectiveness (healthcare provider perspective; 3% discount rate; time horizon 2016-2040) of the current PrEP provision., Results: Calibrated to national data, model projections suggest that 2.1% of HIV-negative FSWs were currently on PrEP in 2020, with PrEP preventing 0.45% (95% credibility interval, 0.35-0.57%) of HIV infections among FSWs over 2016-2020 or 605 (444-840) infections overall. Reductions in PrEP initiations in 2020 possibly reduced infections averted by 18.57% (13.99-23.29). PrEP is cost-saving, with $1.42 (1.03-1.99) of ART costs saved per dollar spent on PrEP. Going forward, existing coverage of PrEP will avert 5,635 (3,572-9,036) infections by 2040. However, if PrEP initiation and retention doubles, then PrEP coverage increases to 9.9% (8.7-11.6%) and impact increases 4.3 times with 24,114 (15,308-38,107) infections averted by 2040., Conclusions: Our findings advocate for the expansion of PrEP to FSWs throughout SA to maximize its impact. This should include strategies to optimize retention and should target women in contact with FSW services., (© 2023 The Authors. Journal of the International AIDS Society published by John Wiley & Sons Ltd on behalf of the International AIDS Society.)

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics"., Competing Interests: Declaration of Competing Interest ☒The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Ciara E. Dangerfield is the senior scientific programme manager for the JUNIPER consortium and is on secondment from her position at Isaac Newton Institute for the mathematical sciences as the development and communications coordinator. I.David Abrahams is previously director of the Isaac Newton Institute (2016-2021), led the working group to develop a prototype for the National Academy of Mathematical Sciences in the UK, co-led the development of a connected centres for knowledge exchange network for the UK paper, co-investigator on the UKRI funded RAMP continuity network grant and is a forum partner for V-KEMS. Dawn Wasley is knowledge exchange coordinator at ICMS and is a forum partner for V-KEMS. Jane Leeks is the manager of the Newton Gateway, co-led the development of a connected centres for knowledge exchange network for the UK paper and is a forum partner for V-KEMS. Clare Merritt is senior scientific knowledge exchange coordinator at the Newton Gateway and is a forum partner for V-KEMS. Maha Kaouri is scientific knowledge exchange coordinate at the Newton Gateway and is a forum partner for V-KEMS. Christie Marr is deputy director at the Isaac Newton Institute for the mathematical sciences. Julia Gog attended SPI-M, SPI-M-O and SAGE meetings, was co-investigator on the UKRI funded RAMP continuity network grant, is co-principle investigator for the JUNIPER consortium and was an organiser of the Infectious Dynamics of Pandemics research programme at the Isaac Newton Institute. Deirdre Hollingsworth attended SPI-M-O meetings, was co-investigator on the UKRI funded RAMP continuity network grant, is a co-investigator for the JUNIPER consortium, leads the Neglected Tropical Diseases modelling consortium and was principle organiser of the Infectious Dynamics of Pandemics Programme at the Isaac Newton Institute. Chris Budd is director of knowledge exchange for Bath Institute for Mathematical Innovation, Director of the Centre for Nonlinear Mechanics, Fellow of Gresham College, Professor of Mathematics at the Royal Institution of Great Britain and is a forum partner for V-KEMS. Matt Butchers previously part of the Knowledge Transfer Network, currently industrial fellow at Bath Institute for Mathematical Innovation, member of the advisory board for the Newton Gateway, author of the connected centre for knowledge exchange paper and is a forum partner for V-KEMS. Alan Champneys is a member of Newton Gateway scientific advisory panel and a forum partner for V-KEMS. Rebecca Hoyle is a member of Newton Gateway scientific advisory panel and a forum partner for V-KEMS. Joanna Jordan is a freelance mathematical sciences knowledge exchange professional, member of the advisory board for the Newton Gateway, is author of the connected centre for knowledge exchange paper and is a forum partner for V-KEMS. Michael E Cates was principle investigator on the UKRI funded RAMP continuity network grant. Valerie Isham was one of the organisers of the Infectious Dynamics of Pandemics programme at the Isaac Newton Institute and was previously chair of the scientific steering committee at the Isaac Newton Institute for the mathematical sciences. INI Professional Services are predominantly supported through an EPSRC grant no. EP/R014604/1. Christine Currie was part of the working group to develop a prototype for the National Academy of Mathematical Sciences in the UK and is a member of Newton Gateway scientific advisory panel. Alain Goriely is Director of the Oxford Centre for Industrial Applied Mathematics, Director of the International Brain and Mechanics Trauma Lab, Fellow of SIAM and the IMA, and co-investigator on the UKRI funded RAMP continuity network grant. Kostas Kavoussanakis is group manager at EPCC at the University of Edinburgh and co-investigator on the UKRI funded RAMP continuity network grant. Philip K Maini was co-investigator on the UKRI funded RAMP continuity network grant. Denis Mollison was an organiser of the Infectious Dynamics of Pandemics Programme at INI. Surajit Ray is a member of Newton Gateway scientific advisory panel. Alex Wakefield is senior policy advisor and programme manager at the Royal Society. Robin Thompson attended SPI-M-O meetings and is a member of the JUNIPER consortium. Jessica Enright is a member of the JUNIPER consortium., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Introduction: A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures., Methods: Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases., Results: We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population., Discussion: Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Thompson, Southall, Daon, Lovell-Read, Iwami, Thompson and Obolski.)

In this paper, we provide a simple ODEs model with a generic nonlinear incidence rate function and incorporate two treatments, blocking the virus binding and inhibiting the virus replication to investigate the impact of calibration on model predictions for the SARS-CoV-2 infection dynamics. We derive conditions of the infection eradication for the long-term dynamics using the basic reproduction number, and complement the characterization of the dynamics at short-time using the resilience and reactivity of the virus-free equilibrium are considered to inform on the average time of recovery and sensitivity to perturbations in the initial virus free stage. Then, we calibrate the treatment model to clinical datasets for viral load in mild and severe cases and immune cells in severe cases. Based on the analysis, the model calibrated to these different datasets predicts distinct scenarios: eradication with a non reactive virus-free equilibrium, eradication with a reactive virus-free equilibrium, and failure of infection eradication. Moreover, severe cases generate richer dynamics and different outcomes with the same treatment. Calibration to different datasets can lead to diverse model predictions, but combining long- and short-term dynamics indicators allows the categorization of model predictions and determination of infection severity., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Objectives: Over time, papers or reports may come to be taken for granted as evidence for some phenomenon. Researchers cite them without critically re-examining findings in the light of subsequent work. This can give rise to misleading or erroneous results and conclusions. We explore whether this has occurred in the widely reported outbreak of SARS-CoV-2 at a rehearsal of the Skagit Valley Chorale in March 2020, where it was assumed, and subsequently asserted uncritically, that the outbreak was due to a single infected person., Study Design: Review of original report and subsequent modelling and interpretations., Methods: We reviewed and analysed original outbreak data in relation to published data on incubation period, subsequent modelling drawing on the data, and interpretations of transmission characteristics of this incident., Results: We show it is vanishingly unlikely that this was a single point source outbreak as has been widely claimed and on which modelling has been based., Conclusion: An unexamined assumption has led to erroneous policy conclusions about the risks of singing, and indoor spaces more generally, and the benefits of increased levels of ventilation. Although never publicly identified, one individual bears the moral burden of knowing what health outcomes have been attributed to their actions. We call for these claims to be re-examined and for greater ethical responsibility in the assumption of a point source in outbreak investigations., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The recovery of elective waiting lists represents a major challenge and priority for the health services of many countries. In England's National Health Service (NHS), the waiting list has increased by 45% in the two years since the COVID-19 pandemic was declared in March 2020. Long waits associate with worse patient outcomes and can deepen inequalities and lead to additional demands on healthcare resources. Modelling the waiting list can be valuable for both estimating future trajectories and considering alternative capacity allocation strategies. However, there is a deficit within the current literature of scalable solutions that can provide managers and clinicians with hospital and specialty level projections on a routine basis. In this paper, a model representing the key dynamics of the waiting list problem is presented alongside its differential equation based solution. Versatility of the model is demonstrated through its calibration to routine publicly available NHS data. The model has since been used to produce regular monthly projections of the waiting list for every hospital trust and specialty in England., (© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Background: Controlling the epidemic spread and establishing the immune barrier in a short time through accurate vaccine demand prediction and optimised vaccine allocation strategy are still urgent problems to be solved under the condition of frequent virus mutations., Methods: A cross-regional Susceptible-Exposed-Infected-Removed dynamic model was used for scenario simulation to systematically elaborate and compare the effects of different cross-regional vaccine allocation strategies on the future development of the epidemic in regions with different population sizes, prevention and control capabilities, and initial risk levels. Furthermore, the trajectory of the cross-regional vaccine allocation strategy, calculated using a particle swarm optimisation algorithm, was compared with the trajectories of other strategies., Results: By visualising the final effect of the particle swarm optimisation vaccine allocation strategy, this study revealed the important role of prevention and control (including the level of social distancing control, the speed of tracking and isolating exposed and infected individuals, and the initial frequency of mask-wearing) in determining the allocation of vaccine resources. Most importantly, it supported the idea of prioritising control in regions with a large population and low initial risk level, which broke the general view that high initial risk needs to be given priority and proposed that outbreak risk should be firstly considered instead., Conclusions: This is the first study to use a particle swarm optimisation algorithm to study the cross-regional allocation of COVID-19 vaccines. These data provide a theoretical basis for countries and regions to develop more targeted and sustainable vaccination strategies.KEY MESSAGEThe innovative combination of particle swarm optimisation and cross-regional SEIR model to simulate the pandemic trajectory and predict the vaccine demand helped to speed up and stabilise the construction of the immune barrier, especially faced with new virus mutations.We proposed that priority should be given to regions where it is possible to prevent more infections rather than regions where it is at high initial risk, thus regional outbreak risk should be considered when making vaccine allocation decisions.An optimal health-oriented strategy for vaccine allocation in the COVID-19 pandemic is determined considering both pharmaceutical and non-pharmaceutical policy interventions, including speed of isolation, degree of social distancing control, and frequency of mask-wearing.

Contact tracing, where exposed individuals are followed up to break ongoing transmission chains, is a key pillar of outbreak response for infectious disease outbreaks. Unfortunately, these systems are not fully effective, and infections can still go undetected as people may not remember all their contacts or contacts may not be traced successfully. A large proportion of undetected infections suggests poor contact tracing and surveillance systems, which could be a potential area of improvement for a disease response. In this paper, we present a method for estimating the proportion of infections that are not detected during an outbreak. Our method uses next generation matrices that are parameterized by linked contact tracing data and case line-lists. We validate the method using simulated data from an individual-based model and then investigate two case studies: the proportion of undetected infections in the SARS-CoV-2 outbreak in New Zealand during 2020 and the Ebola epidemic in Guinea during 2014. We estimate that only 5.26% of SARS-CoV-2 infections were not detected in New Zealand during 2020 (95% credible interval: 0.243 - 16.0%) if 80% of contacts were under active surveillance but depending on assumptions about the ratio of contacts not under active surveillance versus contacts under active surveillance 39.0% or 37.7% of Ebola infections were not detected in Guinea (95% credible intervals: 1.69 - 87.0% or 1.70 - 80.9%)., Competing Interests: Competing interests None., (Copyright © 2022 The Authors. Published by Elsevier B.V. All rights reserved.)

Background: With the prompt administration of coronavirus disease 2019 (COVID-19) vaccines, highly vaccinated countries have begun to lift their stringent control measures. However, considering the spread of highly transmissible new variants, resuming socio-economic activities may lead to the resurgence of incidence, particularly in nations with a low proportion of individuals who have natural immunity. Here, we aimed to quantitatively assess an optimal COVID-19 exit strategy in the Republic of Korea, where only a small number of cumulative incidences have been recorded as of September 2021, comparing epidemiological outcomes via scenario analysis., Methods: A discrete-time deterministic compartmental model structured by age group was used, accounting for the variant-specific transmission dynamics and the currently planned nationwide vaccination. All parameters were calibrated using comprehensive empirical data obtained from the Korea Disease Control and Prevention Agency., Results: Our projection suggests that tapering the level of social distancing countermeasures to the minimum level from November 2021 can efficiently suppress a resurgence of incidence given the currently planned nationwide vaccine roll-out. In addition, considering the spread of the Delta variant, our model suggested that gradual easing of countermeasures for more than 4 months can efficiently withstand the prevalence of severe COVID-19 cases until the end of 2022., Conclusions: Our model-based projections provide evidence-based guidance for an exit strategy that allows society to resume normal life while sustaining the suppression of the COVID-19 epidemic in countries where the spread of COVID-19 has been well controlled., (© 2022. The Author(s).)

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number ( R t ), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of R t varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide R t , this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on R t estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate R t , made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect R t estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate R t . This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The coronavirus disease 2019 (COVID-19) pandemic has highlighted the importance of mathematical modelling in informing and advising policy decision-making. Effective practice of mathematical modelling has challenges. These can be around the technical modelling framework and how different techniques are combined, the appropriate use of mathematical formalisms or computational languages to accurately capture the intended mechanism or process being studied, in transparency and robustness of models and numerical code, in simulating the appropriate scenarios via explicitly identifying underlying assumptions about the process in nature and simplifying approximations to facilitate modelling, in correctly quantifying the uncertainty of the model parameters and projections, in taking into account the variable quality of data sources, and applying established software engineering practices to avoid duplication of effort and ensure reproducibility of numerical results. Via a collection of 16 technical papers, this special issue aims to address some of these challenges alongside showcasing the usefulness of modelling as applied in this pandemic. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10 -4 -12×10 -4 /h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Inc. All rights reserved.)

The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provide a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the effective reproduction number, [Formula: see text], has taken on special significance in terms of the general understanding of whether the epidemic is under control ([Formula: see text]). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, focusing on the dynamics of the first wave (March-June 2020), we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the time course of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence.

Over the past two decades, vaccination programmes for vaccine-preventable diseases (VPDs) have expanded across low- and middle-income countries (LMICs). However, the rise of COVID-19 resulted in global disruption to routine immunisation activities. Such disruptions could have a detrimental effect on public health, leading to more deaths from VPDs, particularly without mitigation efforts. Hence, as routine immunisation activities resume, it is important to estimate the effectiveness of different approaches for recovery. We apply an impact extrapolation method developed by the Vaccine Impact Modelling Consortium to estimate the impact of COVID-19-related disruptions with different recovery scenarios for ten VPDs across 112 LMICs. We focus on deaths averted due to routine immunisations occurring in the years 2020-2030 and investigate two recovery scenarios relative to a no-COVID-19 scenario. In the recovery scenarios, we assume a 10% COVID-19-related drop in routine immunisation coverage in the year 2020. We then linearly interpolate coverage to the year 2030 to investigate two routes to recovery, whereby the immunization agenda (IA2030) targets are reached by 2030 or fall short by 10%. We estimate that falling short of the IA2030 targets by 10% leads to 11.26% fewer fully vaccinated persons (FVPs) and 11.34% more deaths over the years 2020-2030 relative to the no-COVID-19 scenario, whereas, reaching the IA2030 targets reduces these proportions to 5% fewer FVPs and 5.22% more deaths. The impact of the disruption varies across the VPDs with diseases where coverage expands drastically in future years facing a smaller detrimental effect. Overall, our results show that drops in routine immunisation coverage could result in more deaths due to VPDs. As the impact of COVID-19-related disruptions is dependent on the vaccination coverage that is achieved over the coming years, the continued efforts of building up coverage and addressing gaps in immunity are vital in the road to recovery., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The COVID-19 pandemic caused multiple waves of mortality in South Africa, where three genetic variants of SARS-COV-2 and their ancestral strain dominated consecutively. State-of-the-art mathematical modeling approach was used to estimate the time-varying transmissibility of SARS-COV-2 and the relative transmissibility of Beta, Delta, and Omicron variants. The transmissibility of the three variants were about 73%, 87%, and 276% higher than their preceding variants. To the best of our knowledge, our model is the first simple model that can simulate multiple mortality waves and three variants' replacements in South Africa. The transmissibility of the Omicron variant is substantially higher than that of previous variants.

The COVID-19 pandemic was reported from March 2020 in Zimbabwe. COVID-19 containment measures which included repeated lockdowns have disrupted community interactions, reduced working hours, restricted travel and restricted HIV services for people living with HIV (PLHIV), among others. The study adopted a cross-sectional design. Both qualitative and quantitative data were collected in all the 10 provinces and analysed. A sample size of 480 was calculated for the cross-sectional survey. Secondary data on HIV early warning indicators from 2018 to 2021 were extracted from 20 randomly selected health facilities and used for modelling. Mathematical modelling was conducted to assess the impact of COVID-19 on PLHIV. AIDS-related deaths increased from 20 100 in 2019 to 22 200 in 2020. In addition, there were significant years of life lost (yLLs) from premature mortality and years of life lost due to disability (yLDs) from COVID-19. Prevalence of COVID-19 among PLHIV was 4%. COVID-19 vaccination coverage was 64%, which is higher than the national average of 42%. Stress and breach of confidentiality as ARV medicines were given out in open spaces and fear of contracting COVID-19 were the perceived psychological issues. COVID-19 disrupted HIV service provision, increased AIDS-related deaths and caused psychological challenges.

Background: SARS-CoV-2 is known to transmit in hospital settings, but the contribution of infections acquired in hospitals to the epidemic at a national scale is unknown., Methods: We used comprehensive national English datasets to determine the number of COVID-19 patients with identified hospital-acquired infections (with symptom onset > 7 days after admission and before discharge) in acute English hospitals up to August 2020. As patients may leave the hospital prior to detection of infection or have rapid symptom onset, we combined measures of the length of stay and the incubation period distribution to estimate how many hospital-acquired infections may have been missed. We used simulations to estimate the total number (identified and unidentified) of symptomatic hospital-acquired infections, as well as infections due to onward community transmission from missed hospital-acquired infections, to 31st July 2020., Results: In our dataset of hospitalised COVID-19 patients in acute English hospitals with a recorded symptom onset date (n = 65,028), 7% were classified as hospital-acquired. We estimated that only 30% (range across weeks and 200 simulations: 20-41%) of symptomatic hospital-acquired infections would be identified, with up to 15% (mean, 95% range over 200 simulations: 14.1-15.8%) of cases currently classified as community-acquired COVID-19 potentially linked to hospital transmission. We estimated that 26,600 (25,900 to 27,700) individuals acquired a symptomatic SARS-CoV-2 infection in an acute Trust in England before 31st July 2020, resulting in 15,900 (15,200-16,400) or 20.1% (19.2-20.7%) of all identified hospitalised COVID-19 cases., Conclusions: Transmission of SARS-CoV-2 to hospitalised patients likely caused approximately a fifth of identified cases of hospitalised COVID-19 in the "first wave" in England, but less than 1% of all infections in England. Using time to symptom onset from admission for inpatients as a detection method likely misses a substantial proportion (> 60%) of hospital-acquired infections., (© 2022. The Author(s).)

As the COVID-19 pandemic continues, genetic mutations in SARS-CoV-2 emerge, and some of them are found more contagious than the previously identified strains, acting as the major mechanism for many large-scale epidemics. The transmission advantage of mutated variants is widely believed as an innate biological feature that is difficult to be altered by artificial factors. In this study, we explore how non-pharmaceutical interventions (NPI) may affect transmission advantage. A two-strain compartmental epidemic model is proposed and simulated to investigate the biological mechanism of the relationships among different NPIs, the changes in transmissibility of each strain and transmission advantage. Although the NPIs are effective in flattening the epidemic curve, we demonstrate that NPIs probably lead to a decline in transmission advantage, which is likely to occur if the NPIs become intensive. Our findings uncover the mechanistic relationship between NPIs and transmission advantage dynamically, and highlight the important role of NPIs not only in controlling the intensity of epidemics but also in slowing or even containing the growth of the proportion of variants., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: MHW is a shareholder of Beth Bioinformatics Co., Ltd. Other authors declared no competing interests. The funding agencies had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Background: Managing high levels of acute COVID-19 bed occupancy can affect the quality of care provided to both affected patients and those requiring other hospital services. Mass vaccination has offered a route to reduce societal restrictions while protecting hospitals from being overwhelmed. Yet, early in the mass vaccination effort, the possible impact on future bed pressures remained subject to considerable uncertainty., Objective: The aim of this study was to model the effect of vaccination on projections of acute and intensive care bed demand within a 1 million resident healthcare system located in South West England., Methods: An age-structured epidemiological model of the susceptible-exposed-infectious-recovered type was fitted to local data up to the time of the study, in early March 2021. Model parameters and vaccination scenarios were calibrated through a system-wide multidisciplinary working group, comprising public health intelligence specialists, healthcare planners, epidemiologists and academics. Scenarios assumed incremental relaxations to societal restrictions according to the envisaged UK Government timeline, with all restrictions to be removed by 21 June 2021., Results: Achieving 95% vaccine uptake in adults by 31 July 2021 would not avert the third wave in autumn 2021 but would produce a median peak bed requirement ∼6% (IQR: 1-24%) of that experienced during the second wave (January 2021). A 2-month delay in vaccine rollout would lead to significantly higher peak bed occupancy, at 66% (11-146%) of that of the second wave. If only 75% uptake was achieved (the amount typically associated with vaccination campaigns), then the second wave peak for acute and intensive care beds would be exceeded by 4% and 19%, respectively, an amount which would seriously pressure hospital capacity., Conclusion: Modelling influenced decision-making among senior managers in setting COVID-19 bed capacity levels, as well as highlighting the importance of public health in promoting high vaccine uptake among the population. Forecast accuracy has since been supported by actual data collected following the analysis, with observed peak bed occupancy falling comfortably within the inter-quartile range of modelled projections., (© The Author(s) 2022. Published by Oxford University Press on behalf of International Society for Quality in Health Care. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

This paper presents a method used to rapidly assess the incursion and the establishment of community transmission of suspected SARS-CoV-2 variant of concern Delta (lineage B.1.617.2) into the UK in April and May 2021. The method described is independent of any genetically sequenced data, and so avoids the inherent lag times involved in sequencing of cases. We show that, between 1 April and 12 May 2021, there was a strong correlation between local authorities with high numbers of imported positive cases from India and high COVID-19 case rates, and that this relationship holds as we look at finer geographic detail. Further, we also show that Bolton was an outlier in the relationship, having the highest COVID-19 case rates despite relatively few importations. We use an artificial neural network trained on demographic data, to show that observed importations in Bolton were consistent with similar areas. Finally, using an SEIR transmission model, we show that imported positive cases were a contributing factor to persistent transmission in a number of local authorities, however they could not account for increased case rates observed in Bolton. As such, the outbreak of Delta variant in Bolton was likely not a result of direct importation from overseas, but rather secondary transmission from other regions within the UK.

Mathematical modelling has been a helpful resource for planning public health responses to COVID-19. However, there is a need to improve the accessibility of models built within country contexts in the Global South. Immediately following the overwhelming 'second wave' of COVID-19 in India, we developed a user-friendly, web-based modelling simulator in partnership with the public health experts and health administrators for subnational planning. The purpose was to help policy-makers and programme officials at the state and district levels, to construct model-based scenarios for a possible third wave. Here, we describe our experiences of developing and deploying the simulator and propose the following recommendations for future such initiatives: early preparation will be the key for pandemic management planning, including establishment of networks with potential simulator users. Ideally, this preparedness should be conducted during 'peace time', and coordinated by agencies such as WHO. Second, flexible modelling frameworks will be needed, to respond rapidly to future emergencies as the precise nature of any pandemic is impossible to predict. Modelling resources will, therefore, need to be rapidly adaptable to respond as soon as a novel pathogen emerges. Third, limitations of modelling must be communicated clearly and consistently to end users. Finally, systematic mechanisms are required for monitoring the use of models in decision making, which will help in providing modelling support to those local authorities who may benefit most from it. Overall, these lessons from India can be relevant for other countries in the South-Asian-Region, to incorporate modelling resources into their pandemic preparedness planning., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2022. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Deciphering the properties of vaccines against an emerging pathogen is essential for optimizing immunization strategies. Early after vaccine roll-out, however, uncertainties about vaccine immunity raise the question of how much time is needed to estimate these properties, particularly the durability of vaccine protection. Here we designed a simulation study, based on a generic transmission model of vaccination, to simulate the impact of a breadth of vaccines with different mean (range: 10 months-2 years) and variability (coefficient of variation range: 50-100%) of the duration of protection. Focusing on the dynamics of SARS-CoV-2 in the year after start of mass immunization in Germany as a case study, we then assessed how confidently the duration of protection could be estimated under a range of epidemiological scenarios. We found that lower mean and higher heterogeneity facilitated estimation of the duration of vaccine protection. Across the vaccines tested, rapid waning and high heterogeneity permitted complete identification of the duration of protection; by contrast, slow waning and low heterogeneity allowed only estimation of the fraction of vaccinees with rapid loss of immunity. These findings suggest that limited epidemiological data can inform the duration of vaccine immunity. More generally, they highlight the need to carefully consider immunological heterogeneity when designing transmission models to evaluate vaccines.

The coronavirus disease 2019 (COVID-19) pandemic had an uneven development in different countries. In Argentina, the pandemic began in March 2020 and, during the first 3 months, the vast majority of cases were concentrated in a densely populated region that includes the city of Buenos Aires (country capital) and the Greater Buenos Aires (GBA) area that surrounds it. This work focuses on the spread of COVID-19 between June and November 2020 in GBA. Within this period of time there was no vaccine, basically only the early wild strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was present, and the official restriction and distancing measures in this region remained more or less constant. Under these particular conditions, the incidences show a sharp rise from June 2020 and begin to decrease towards the end of August until the end of November 2020. In this work we study, through mathematical modelling and available epidemiological information, the spread of COVID-19 in this region and period of time. We show that a coherent explanation of the evolution of incidences can be obtained assuming that only a minority fraction of the population got involved in the spread process, so that the incidences decreased as this group of people was becoming immune. The observed evolution of the incidences could then be a consequence at the population level of lasting immunity conferred by SARS-CoV-2.

During the first wave of the COVID-19 pandemic, sub-Saharan African countries experienced comparatively lower rates of SARS-CoV-2 infections and related deaths than in other parts of the world, the reasons for which remain unclear. Yet, there was also considerable variation between countries. Here, we explored potential drivers of this variation among 46 of the 47 WHO African region Member States in a cross-sectional study. We described five indicators of early COVID-19 spread and severity for each country as of 29 November 2020: delay in detection of the first case, length of the early epidemic growth period, cumulative and peak attack rates and crude case fatality ratio (CFR). We tested the influence of 13 pre-pandemic and pandemic response predictor variables on the country-level variation in the spread and severity indicators using multivariate statistics and regression analysis. We found that wealthier African countries, with larger tourism industries and older populations, had higher peak (p<0.001) and cumulative (p<0.001) attack rates, and lower CFRs (p=0.021). More urbanised countries also had higher attack rates (p<0.001 for both indicators). Countries applying more stringent early control policies experienced greater delay in detection of the first case (p<0.001), but the initial propagation of the virus was slower in relatively wealthy, touristic African countries (p=0.023). Careful and early implementation of strict government policies were likely pivotal to delaying the initial phase of the pandemic, but did not have much impact on other indicators of spread and severity. An over-reliance on disruptive containment measures in more resource-limited contexts is neither effective nor sustainable. We thus urge decision-makers to prioritise the reduction of resource-based health disparities, and surveillance and response capacities in particular, to ensure global resilience against future threats to public health and economic stability., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2022. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

The emergence of new SARS-CoV-2 variants of concern (VOC) has hampered international efforts to contain the COVID-19 pandemic. VOCs have been characterized to varying degrees by higher transmissibility, worse infection outcomes and evasion of vaccine and infection-induced immunologic memory. VOCs are hypothesized to have originated from animal reservoirs, communities in regions with low surveillance and/or single individuals with poor immunologic control of the virus. Yet, the factors dictating which variants ultimately predominate remain incompletely characterized. Here we present a multi-scale model of SARS-CoV-2 dynamics that describes population spread through individuals whose viral loads and numbers of contacts (drawn from an over-dispersed distribution) are both time-varying. This framework allows us to explore how super-spreader events (SSE) (defined as greater than five secondary infections per day) contribute to variant emergence. We find stochasticity remains a powerful determinant of predominance. Variants that predominate are more likely to be associated with higher infectiousness, an SSE early after variant emergence and ongoing decline of the current dominant variant. Additionally, our simulations reveal that most new highly infectious variants that infect one or a few individuals do not achieve permanence in the population. Consequently, interventions that reduce super-spreading may delay or mitigate emergence of VOCs.