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The role of direct cell-to-cell spread in viral infections-where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment-has come to be understood as essential to the dynamics of medically significant viruses like hepatitis C and influenza. Recent work in both the experimental and mathematical modelling literature has attempted to quantify the prevalence of cell-to-cell infection compared to the conventional free virus route using a variety of methods and experimental data. However, estimates are subject to significant uncertainty and moreover rely on data collected by inhibiting one mode of infection by either chemical or physical factors, which may influence the other mode of infection to an extent which is difficult to quantify. In this work, we conduct a simulation-estimation study to probe the practical identifiability of the proportion of cell-to-cell infection, using two standard mathematical models and synthetic data that would likely be realistic to obtain in the laboratory. We show that this quantity cannot be estimated using non-spatial data alone, and that the collection of data which describes the spatial structure of the infection is necessary to infer the proportion of cell-to-cell infection. Our results provide guidance for the design of relevant experiments and mathematical tools for accurately inferring the prevalence of cell-to-cell infection in in vitro and in vivo contexts.

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should f

Freya Shearer and co-authors discuss the use of decision analysis in planning for infectious disease pandemics.

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

BACKGROUND: Effective response to emerging infectious disease (EID) threats relies on health care systems that can detect and contain localised outbreaks before they reach a national or international scale. The Asia-Pacific region contains low and middle income countries in which the risk of EID outbreaks is elevated and whose health care systems may require international support to effectively detect and respond to such events. The absence of comprehensive data on populations, health care systems and disease characteristics in this region makes risk assessment and decisions about the provision of such support challenging. METHODOLOGY/PRINCIPAL FINDINGS: We describe a mathematical modelling framework that can inform this process by integrating available data sources, systematically explore the effects of uncertainty, and provide estimates of outbreak risk under a range of intervention scenarios. We illustrate the use of this framework in the context of a potential importation of Ebola Virus Disease into the Asia-Pacific region. Results suggest that, across a wide range of plausible scenarios, preemptive interventions supporting the timely detection of early cases provide substantially greater reductions in the probability of large outbreaks than interventions that support health care system capacity after an outbreak has commenced. CONCLUSIONS/SIGNIFICANCE: Our study demonstrates how, in the presence of substantial uncertainty about health care system infrastructure and other relevant aspects of disease control, mathematical models can be used to assess the constraints that limited resources place upon the ability of local health care systems to detect and respond to EID outbreaks in a timely and effective fashion. Our framework can help evaluate the relative impact of these constraints to identify resourcing priorities for health care system support, in order to inform principled and quantifiable decision making.

Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus-innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure exper

Successful control of falciparum malaria depends greatly on treatment with artemisinin combination therapies. Thus, reports that resistance to artemisinins (ARTs) has emerged, and that the prevalence of this resistance is increasing, are alarming. ART resistance has recently been linked to mutations in the K13 propeller protein. We undertook a detailed kinetic analysis of the drug responses of K13 wild-type and mutant isolates of Plasmodium falciparum sourced from a region in Cambodia (Pailin). We demonstrate that ART treatment induces growth retardation and an accumulation of ubiquitinated proteins, indicative of a cellular stress response that engages the ubiquitin/proteasome system. We show that resistant parasites exhibit lower levels of ubiquitinated proteins and delayed onset of cell death, indicating an enhanced cell stress response. We found that the stress response can be targeted by inhibiting the proteasome. Accordingly, clinically used proteasome inhibitors strongly synergize ART activity against both sensitive and resistant parasites, including isogenic lines expressing mutant or wild-type K13. Synergy is also observed against Plasmodium berghei in vivo. We developed a detailed model of parasite responses that enables us to infer, for the first time, in vivo parasite clearance profiles from in vitro assessments of ART sensitivity. We provide evidence that the clinical marker of resistance (delayed parasite clearance) is an indirect measure of drug efficacy because of the persistence of unviable parasites with unchanged morphology in the circulation, and we suggest alternative approaches for the direct measurement of viability. Our model predicts that extending current three-day ART treatment courses to four days, or splitting the doses, will efficiently clear resistant parasite infections. This work provides a rationale for improving the detection of ART resistance in the field and for treatment strategies that can be employed in areas with ART resistan

Vaccines that trigger an influenza-specific cytotoxic T cell (CTL) response may aid pandemic control by limiting the transmission of novel influenza A viruses (IAV). We consider interventions with hypothetical CTL-inducing vaccines in a range of epidemiologically plausible pandemic scenarios. We estimate the achievable reduction in the attack rate, and, by adopting a model linking epidemic progression to the emergence of IAV variants, the opportunity for antigenic drift. We demonstrate that CTL-inducing vaccines have limited utility for modifying population-level outcomes if influenza-specific T cells found widely in adults already suppress transmission and prove difficult to enhance. Administration of CTL-inducing vaccines that are efficacious in "influenza-experienced" and "influenza-naive" hosts can likely slow transmission sufficiently to mitigate a moderate IAV pandemic. However if neutralising cross-reactive antibody to an emerging IAV are common in influenza-experienced hosts, as for the swine-variant H3N2v, boosting CTL immunity may be ineffective at reducing population spread, indicating that CTL-inducing vaccines are best used against novel subtypes such as H7N9. Unless vaccines cannot readily suppress transmission from infected hosts with naive T cell pools, targeting influenza-naive hosts is preferable. Such strategies are of enhanced benefit if naive hosts are typically intensively mixing children and when a subset of experienced hosts have pre-existing neutralising cross-reactive antibody. We show that CTL-inducing vaccination campaigns may have greater power to suppress antigenic drift than previously suggested, and targeting adults may be the optimal strategy to achieve this when the vaccination campaign does not have the power to curtail the attack rate. Our results highlight the need to design interventions based on pre-existing cellular immunity and knowledge of the host determinants of vaccine efficacy, and provide a framework for assessing the p

Predicting population dynamics for rare species is of paramount importance in order to evaluate the likelihood of extinction and planning conservation strategies. However, evaluating and predicting population viability can be hindered from a lack of data. Rare species frequently have small populations, so estimates of vital rates are often very uncertain due to lack of data. We evaluated the vital rates of seven small populations from two watersheds with varying light environment of a common epiphytic orchid using Bayesian methods of parameter estimation. From the Lefkovitch matrices we predicted the deterministic population growth rates, elasticities, stable stage distributions and the credible intervals of the statistics. Populations were surveyed on a monthly basis between 18-34 months. In some of the populations few or no transitions in some of the vital rates were observed throughout the sampling period, however, we were able to predict the most likely vital rates using a Bayesian model that incorporated the transitions rates from the other populations. Asymptotic population growth rate varied among the seven orchid populations. There was little difference in population growth rate among watersheds even though it was expected because of physical differences as a result of differing canopy cover and watershed width. Elasticity analyses of Lepanthes rupestris suggest that growth rate is more sensitive to survival followed by growth, shrinking and the reproductive rates. The Bayesian approach helped to estimate transition probabilities that were uncommon or variable in some populations. Moreover, it increased the precision of the parameter estimates as compared to traditional approaches.

Oseltamivir is relied upon worldwide as the drug of choice for the treatment of human influenza infection. Surveillance for oseltamivir resistance is routinely performed to ensure the ongoing efficacy of oseltamivir against circulating viruses. Since the emergence of the pandemic 2009 A(H1N1) influenza virus (A(H1N1)pdm09), the proportion of A(H1N1)pdm09 viruses that are oseltamivir resistant (OR) has generally been low. However, a cluster of OR A(H1N1)pdm09 viruses, encoding the neuraminidase (NA) H275Y oseltamivir resistance mutation, was detected in Australia in 2011 amongst community patients that had not been treated with oseltamivir. Here we combine a competitive mixtures ferret model of influenza infection with a mathematical model to assess the fitness, both within and between hosts, of recent OR A(H1N1)pdm09 viruses. In conjunction with data from in vitro analyses of NA expression and activity we demonstrate that contemporary A(H1N1)pdm09 viruses are now more capable of acquiring H275Y without compromising their fitness, than earlier A(H1N1)pdm09 viruses circulating in 2009. Furthermore, using reverse engineered viruses we demonstrate that a pair of permissive secondary NA mutations, V241I and N369K, confers robust fitness on recent H275Y A(H1N1)pdm09 viruses, which correlated with enhanced surface expression and enzymatic activity of the A(H1N1)pdm09 NA protein. These permissive mutations first emerged in 2010 and are now present in almost all circulating A(H1N1)pdm09 viruses. Our findings suggest that recent A(H1N1)pdm09 viruses are now more permissive to the acquisition of H275Y than earlier A(H1N1)pdm09 viruses, increasing the risk that OR A(H1N1)pdm09 will emerge and spread worldwide.

Surveillance data indicate that most circulating A(H1N1)pdm09 influenza viruses have remained antigenically similar since they emerged in humans in 2009. However, antigenic drift is likely to occur in the future in response to increasing population immunity induced by infection or vaccination. In this study, sequential passaging of A(H1N1)pdm09 virus by contact transmission through two independent series of suboptimally vaccinated ferrets resulted in selection of variant viruses with an amino acid substitution (N156K, H1 numbering without signal peptide; N159K, H3 numbering without signal peptide; N173K, H1 numbering from first methionine) in a known antigenic site of the viral HA. The N156K HA variant replicated and transmitted efficiently between naïve ferrets and outgrew wildtype virus in vivo in ferrets in the presence and absence of immune pressure. In vitro, in a range of cell culture systems, the N156K variant rapidly adapted, acquiring additional mutations in the viral HA that also potentially affected antigenic properties. The N156K escape mutant was antigenically distinct from wildtype virus as shown by binding of HA-specific antibodies. Glycan binding assays demonstrated the N156K escape mutant had altered receptor binding preferences compared to wildtype virus, which was supported by computational modeling predictions. The N156K substitution, and culture adaptations, have been detected in human A(H1N1)pdm09 viruses with N156K preferentially reported in sequences from original clinical samples rather than cultured isolates. This study demonstrates the ability of the A(H1N1)pdm09 virus to undergo rapid antigenic change to evade a low level vaccine response, while remaining fit in a ferret transmission model of immunization and infection. Furthermore, the potential changes in receptor binding properties that accompany antigenic changes highlight the importance of routine characterization of clinical samples in human A(H1N1)pdm09 influenza surveillance.

For in vivo studies of influenza dynamics where within-host measurements are fit with a mathematical model, infectivity assays (e.g. 50% tissue culture infectious dose; TCID50) are often used to estimate the infectious virion concentration over time. Less frequently, measurements of the total (infectious and non-infectious) viral particle concentration (obtained using real-time reverse transcription-polymerase chain reaction; rRT-PCR) have been used as an alternative to infectivity assays. We investigated the degree to which measuring both infectious (via TCID50) and total (via rRT-PCR) viral load allows within-host model parameters to be estimated with greater consistency and reduced uncertainty, compared with fitting to TCID50 data alone. We applied our models to viral load data from an experimental ferret infection study. Best-fit parameter estimates for the "dual-measurement" model are similar to those from the TCID50-only model, with greater consistency in best-fit estimates across different experiments, as well as reduced uncertainty in some parameter estimates. Our results also highlight how variation in TCID50 assay sensitivity and calibration may hinder model interpretation, as some parameter estimates systematically vary with known uncontrolled variations in the assay. Our techniques may aid in drawing stronger quantitative inferences from in vivo studies of influenza virus dynamics.

BACKGROUND: Realistic models of disease transmission incorporating complex population heterogeneities require input from quantitative population mixing studies. We use contact diaries to assess the relative importance of social settings in respiratory pathogen spread using three measures of person contact hours (PCH) as proxies for transmission risk with an aim to inform bipartite network models of respiratory pathogen transmission. METHODS AND FINDINGS: Our survey examines the contact behaviour for a convenience sample of 65 adults, with each encounter classified as occurring in a work, retail, home, social, travel or "other" setting. The diary design allows for extraction of PCH-interaction (cumulative time in face-face conversational or touch interaction with contacts)--analogous to the contact measure used in several existing surveys--as well as PCH-setting (product of time spent in setting and number of people present) and PCH-reach (product of time spent in setting and number of people in close proximity). Heterogeneities in day-dependent distribution of risk across settings are analysed using partitioning and cluster analyses and compared between days and contact measures. Although home is typically the highest-risk setting when PCH measures isolate two-way interactions, its relative importance compared to social and work settings may reduce when adopting a more inclusive contact measure that considers the number and duration of potential exposure events. CONCLUSIONS: Heterogeneities in location-dependent contact behaviour as measured by contact diary studies depend on the adopted contact definition. We find that contact measures isolating face-face conversational or touch interactions suggest that contact in the home dominates, whereas more inclusive contact measures indicate that home and work settings may be of higher importance. In the absence of definitive knowledge of the contact required to facilitate transmission of various respiratory pathogens, it i

BACKGROUND: Many countries have amassed antiviral stockpiles for pandemic preparedness. Despite extensive trial data and modelling studies, it remains unclear how to make optimal use of antiviral stockpiles within the constraints of healthcare infrastructure. Modelling studies informed recommendations for liberal antiviral distribution in the pandemic phase, primarily to prevent infection, but failed to account for logistical constraints clearly evident during the 2009 H1N1 outbreaks. Here we identify optimal delivery strategies for antiviral interventions accounting for logistical constraints, and so determine how to improve a strategy's impact. METHODS AND FINDINGS: We extend an existing SEIR model to incorporate finite diagnostic and antiviral distribution capacities. We evaluate the impact of using different diagnostic strategies to decide to whom antivirals are delivered. We then determine what additional capacity is required to achieve optimal impact. We identify the importance of sensitive and specific case ascertainment in the early phase of a pandemic response, when the proportion of false-positive presentations may be high. Once a substantial percentage of ILI presentations are caused by the pandemic strain, identification of cases for treatment on syndromic grounds alone results in a greater potential impact than a laboratory-dependent strategy. Our findings reinforce the need for a decentralised system capable of providing timely prophylaxis. CONCLUSIONS: We address specific real-world issues that must be considered in order to improve pandemic preparedness policy in a practical and methodologically sound way. Provision of antivirals on the scale proposed for an effective response is infeasible using traditional public health outbreak management and contact tracing approaches. The results indicate to change the transmission dynamics of an influenza epidemic with an antiviral intervention, a decentralised system is required for contact identification and

We present a method to measure the relative transmissibility ("transmission fitness") of one strain of a pathogen compared to another. The model is applied to data from "competitive mixtures" experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond infl

BACKGROUND: Wide-scale use of antiviral agents in the event of an influenza pandemic is likely to promote the emergence of drug resistance, with potentially deleterious effects for outbreak control. We explored factors promoting resistance within a dynamic infection model, and considered ways in which one or two drugs might be distributed to delay the spread of resistant strains or mitigate their impact. METHODS AND FINDINGS: We have previously developed a novel deterministic model of influenza transmission that simulates treatment and targeted contact prophylaxis, using a limited stockpile of antiviral agents. This model was extended to incorporate subclinical infections, and the emergence of resistant virus strains under the selective pressure imposed by various uses of one or two antiviral agents. For a fixed clinical attack rate, R(0) rises with the proportion of subclinical infections thus reducing the number of infections amenable to treatment or prophylaxis. In consequence, outbreak control is more difficult, but emergence of drug resistance is relatively uncommon. Where an epidemic may be constrained by use of a single antiviral agent, strategies that combine treatment and prophylaxis are most effective at controlling transmission, at the cost of facilitating the spread of resistant viruses. If two drugs are available, using one drug for treatment and the other for prophylaxis is more effective at preventing propagation of mutant strains than either random allocation or drug cycling strategies. Our model is relatively straightforward, and of necessity makes a number of simplifying assumptions. Our results are, however, consistent with the wider body of work in this area and are able to place related research in context while extending the analysis of resistance emergence and optimal drug use within the constraints of a finite drug stockpile. CONCLUSIONS: Combined treatment and prophylaxis represents optimal use of antiviral agents to control transmission, at

BACKGROUND: The clinical attack rate of influenza is influenced by prior immunity and mixing patterns in the host population, and also by the proportion of infections that are asymptomatic. This complexity makes it difficult to directly estimate R(0) from the attack rate, contributing to uncertainty in epidemiological models to guide pandemic planning. We have modelled multiple wave outbreaks of influenza from different populations to allow for changing immunity and asymptomatic infection and to make inferences about R(0). DATA AND METHODS: On the island of Tristan da Cunha (TdC), 96% of residents reported illness during an H3N2 outbreak in 1971, compared with only 25% of RAF personnel in military camps during the 1918 H1N1 pandemic. Monte Carlo Markov Chain (MCMC) methods were used to estimate model parameter distributions. FINDINGS: We estimated that most islanders on TdC were non-immune (susceptible) before the first wave, and that almost all exposures of susceptible persons caused symptoms. The median R(0) of 6.4 (95% credibility interval 3.7-10.7) implied that most islanders were exposed twice, although only a minority became ill in the second wave because of temporary protection following the first wave. In contrast, only 51% of RAF personnel were susceptible before the first wave, and only 38% of exposed susceptibles reported symptoms. R(0) in this population was also lower [2.9 (2.3-4.3)], suggesting reduced viral transmission in a partially immune population. INTERPRETATION: Our model implies that the RAF population was partially protected before the summer pandemic wave of 1918, arguably because of prior exposure to interpandemic influenza. Without such protection, each symptomatic case of influenza would transmit to between 2 and 10 new cases, with incidence initially doubling every 1-2 days. Containment of a novel virus could be more difficult than hitherto supposed.