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In this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional‐order derivative operator. The model's existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, R0. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease‐free and endemic equilibrium points. Finally, the numerical solution of the model is executed employing the efficient and widely known Adams‐type predictor‐corrector iterative scheme, and simulation is conducted to investigate the impact of memory index and diverse preventive measures on the occurrence of the disease. Numerical simulation of the model indicates that quarantine, vaccination, and treatment can reduce the numbers of infectious and exposed populations, thereby controlling the disease. Therefore, it is recommended that the government provide financial assistance for vaccine distribution. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel normalized time-fractional susceptible–infected–removed (SIR) model that incorporates memory effects into epidemiological dynamics. The proposed model is based on a newly developed normalized time-fractional derivative, which is similar to the well-known Caputo fractional derivative but is characterized by the property that the sum of its weight function equals one. This unity property is crucial because it helps with evaluating how the fractional order influences the behavior of time-fractional differential equations over time. The normalized time-fractional derivative, with its unity property, provides an intuitive understanding of how fractional orders influence the SIR model's dynamics and enables systematic exploration of how changes in the fractional order affect the model's behavior. We numerically investigate how these variations impact the epidemiological dynamics of our normalized time-fractional SIR model and highlight the role of fractional order in improving the accuracy of infectious disease predictions. The appendix provides the program code for the model. [ABSTRACT FROM AUTHOR]

Plant viruses threaten food security and are often transmitted by insect vectors. Non-persistently transmitted (NPT) plant viruses are transmitted almost exclusively by aphids. Because virions attach to the aphid's stylet (mouthparts) and are acquired and inoculated via brief epidermal probes, the aphid–virus interaction is highly transient, with a very short aphid virus retention time. Many NPT viruses manipulate their host plant's phenotype to change aphid behaviour to optimise virus transmission. Epidemiological models of this have overlooked a key feature of aphid NPT virus retention: probing or feeding on a plant causes aphids to lose the virus. Furthermore, experimental studies suggest aphids could possibly inoculate multiple healthy plants within one infective period if they do not feed. Consequences of this for virus manipulation of host plant phenotype have not been explored. Our new compartmental epidemiological model includes both behaviour-based aphid dispersal and infectivity loss rates, and the ability of infective aphids to probe multiple plants before virus loss. We use our model to explore how NPT virus-induced host phenotypes affect epidemic outcomes, comparing these results to representative previous models. We find that previous models behave fundamentally differently and underestimate the benefit of an 'attract-and-deter' phenotype, where the virus induces increased aphid attraction to infected plants but deters them from prolonged feeding. Our results also highlight the importance of characterising NPT virus retention upon the aphid during probing. Allowing for multiple infective probes increases disease incidence and the effectiveness of virus manipulation, with implications for epidemic prediction and control. Author summary: Plant viruses can cause devastating disease epidemics. Non-persistently transmitted viruses are almost always vectored (transmitted between plants) by aphids. Experiments show virus infection can affect whether aphids are attracted to plants (by altering how infected plants 'smell'), as well as whether aphids settle for an extended feed after a brief initial probe (by altering how infected plants 'taste'). Since virus transmission requires an individual aphid to briefly probe an infected plant followed by one or more healthy plant(s), this strongly affects disease transmission. However, most studies exploring virus epidemics do not account for how aphid feeding behaviour affects how long an aphid holds the virus for, or that an aphid could infect multiple healthy plants before losing the virus. We use mathematical modelling to dissect how these aspects of aphid feeding behaviour affect virus transmission, particularly when viruses manipulate the 'smell' and 'taste' of plants. We show how previous studies, by omitting crucial aspects of aphid feeding behaviour, underestimate how viruses can promote their own transmission. We also highlight that there are very few experimental studies exploring the number of plants an aphid with the virus can consecutively infect, which is a key parameter affecting the severity of epidemics. [ABSTRACT FROM AUTHOR]

Background: COVID-19 will not be the last pandemic of the twenty-first century. To better prepare for the next one, it is essential that we make honest appraisals of the utility of different responses to COVID. In this paper, we focus specifically on epidemiologic forecasting. Characterizing forecast efficacy over the history of the pandemic is challenging, especially given its significant spatial, temporal, and contextual variability. In this light, we introduce the Weighted Contextual Interval Score (WCIS), a new method for retrospective interval forecast evaluation. Methods: The central tenet of the WCIS is a direct incorporation of contextual utility into the evaluation. This necessitates a specific characterization of forecast efficacy depending on the use case for predictions, accomplished via defining a utility threshold parameter. This idea is generalized to probabilistic interval-form forecasts, which are the preferred prediction format for epidemiological modeling, as an extension of the existing Weighted Interval Score (WIS). Results: We apply the WCIS to two forecasting scenarios: facility-level hospitalizations for a single state, and state-level hospitalizations for the whole of the United States. We observe that an appropriately parameterized application of the WCIS captures both the relative quality and the overall frequency of useful forecasts. Since the WCIS represents the utility of predictions using contextual normalization, it is easily comparable across highly variable pandemic scenarios while remaining intuitively representative of the in-situ quality of individual forecasts. Conclusions: The WCIS provides a pragmatic utility-based characterization of probabilistic predictions. This method is expressly intended to enable practitioners and policymakers who may not have expertise in forecasting but are nevertheless essential partners in epidemic response to use and provide insightful analysis of predictions. We note that the WCIS is intended specifically for retrospective forecast evaluation and should not be used as a minimized penalty in a competitive context as it lacks statistical propriety. Code and data used for our analysis are available at https://github.com/maximilian-marshall/wcis. [ABSTRACT FROM AUTHOR]

During various stages of the COVID‐19 pandemic, countries implemented diverse vaccine management approaches, influenced by variations in infrastructure and socio‐economic conditions. This article provides a comprehensive overview of optimization models developed by the research community throughout the COVID‐19 era, aimed at enhancing vaccine distribution and establishing a standardized framework for future pandemic preparedness. These models address critical issues such as site selection, inventory management, allocation strategies, distribution logistics, and route optimization encountered during the COVID‐19 crisis. A unified framework is employed to describe the models, emphasizing their integration with epidemiological models to facilitate a holistic understanding. This article also summarizes evolving nature of literature, relevant research gaps, and authors' perspectives for model selection. Finally, future research scopes are detailed both in the context of modeling and solutions approaches. [ABSTRACT FROM AUTHOR]

In this work, we derive a system of Boltzmann-type equations to describe the spread of contact-based infections, such as SARS-CoV-2 virus, at the microscopic scale, that is, by modeling the human-to-human mechanisms of transmission. To this end, we consider two populations, characterized by specific distribution functions, made up of individuals without symptoms (population 1) and infected people with symptoms (population 2). The Boltzmann operators model the interactions between individuals within the same population and among different populations with a probability of transition from one to the other due to contagion or, vice versa, to recovery. In addition, the influence of innate and adaptive immune systems is taken into account. Then, starting from the Boltzmann microscopic description we derive a set of evolution equations for the size and mean state of each population considered. Mathematical properties of such macroscopic equations, as equilibria and their stability, are investigated, and some numerical simulations are performed in order to analyze the ability of our model to reproduce the characteristic features of Covid-19 type pandemics. [ABSTRACT FROM AUTHOR]

In this work, we investigate the numerical performance of a continuous data assimilation algorithm based on ideas from the feedback control theory of dynamical systems, in the context of the SEIR (Susceptible-Exposed-Infectious-Recovered) compartmental mathematical model of epidemics. The motivation behind this work is to propose a new approach that estimates the infection rate parameter in the SEIR model. However, this model may have limited predictive value due to the idealized assumptions underlying it and measurement errors in the experimental data and parameters. We first implement this model as a paradigm because of its application to more realistic epidemic models, then we present our theoretical results. In addition, we provide numerous numerical simulations and significant examples to illustrate the first part of our work. [ABSTRACT FROM AUTHOR]

Background: To make the best use of health resources, it is crucial to understand the healthcare needs of a population—including how needs will evolve and respond to changing epidemiological context and patient behaviour—and how this compares to the capabilities to deliver healthcare with the existing workforce. Existing approaches to planning either rely on using observed healthcare demand from a fixed historical period or using models to estimate healthcare needs within a narrow domain (e.g., a specific disease area or health programme). A new data-grounded modelling method is proposed by which healthcare needs and the capabilities of the healthcare workforce can be compared and analysed under a range of scenarios: in particular, when there is much greater propensity for healthcare seeking. Methods: A model representation of the healthcare workforce, one that formalises how the time of the different cadres is drawn into the provision of units of healthcare, was integrated with an individual-based epidemiological model—the Thanzi La Onse model—that represents mechanistically the development of disease and ill-health and patients' healthcare seeking behaviour. The model was applied in Malawi using routinely available data and the estimates of the volume of health service delivered were tested against officially recorded data. Model estimates of the "time needed" and "time available" for each cadre were compared under different assumptions for whether vacant (or established) posts are filled and healthcare seeking behaviour. Results: The model estimates of volume of each type of service delivered were in good agreement with the available data. The "time needed" for the healthcare workforce greatly exceeded the "time available" (overall by 1.82-fold), especially for pharmacists (6.37-fold) and clinicians (2.83-fold). This discrepancy would be largely mitigated if all vacant posts were filled, but the large discrepancy would remain for pharmacists (2.49-fold). However, if all of those becoming ill did seek care immediately, the "time needed" would increase dramatically and exceed "time supply" (2.11-fold for nurses and midwives, 5.60-fold for clinicians, 9.98-fold for pharmacists) even when there were no vacant positions. Conclusions: The results suggest that services are being delivered in less time on average than they should be, or that healthcare workers are working more time than contracted, or a combination of the two. Moreover, the analysis shows that the healthcare system could become overwhelmed if patients were more likely to seek care. It is not yet known what the health consequences of such changes would be but this new model provides—for the first time—a means to examine such questions. [ABSTRACT FROM AUTHOR]

Infection duration affects individual host fitness and between-host transmission. Whether an infection is cleared or becomes chronic depends on the complex interaction between host immune responses and parasite growth. Empirical and theoretical studies have suggested that there are critical thresholds of parasite dose that can determine clearance versus chronicity, driven by the ability of the parasite to manipulate host immunity. However, the mammalian immune response is characterized by strong positive and negative feedback loops that could generate duration thresholds even in the absence of direct immunomodulation. Here, we derive and analyse a simple model for the interaction between T-cell subpopulations and parasite growth. We show that whether an infection is cleared or not is very sensitive to the initial immune state, parasite dose and strength of immunological feedbacks. In particular, chronic infections are possible even when parasites provoke a strong and effective immune response and lack any ability to immunomodulate. Our findings indicate that the initial immune state, which often goes unmeasured in empirical studies, is a critical determinant of infection duration. This work also has implications for epidemiological models, as it implies that infection duration will be highly variable among individuals, and dependent on each individual's infection history. [ABSTRACT FROM AUTHOR]

Pathogens such as bacteria, fungi and viruses are important components of soil and aquatic communities, where they can benefit from decaying and living organic matter, and may opportunistically infect human and animal hosts. One-third of human infectious diseases is constituted by sapronotic disease agents that are natural inhabitants of soil or aquatic ecosystems. They are capable of existing and reproducing in the environment outside of the host for extended periods of time. However, as ecological research on sapronosis is infrequent and epidemiological models are even rarer, very little information is currently available. Their importance is overlooked in medical and veterinary research, as well as the relationships between free environmental forms and those that are pathogenic. Here, using dynamical models in realistic aquatic metacommunity systems, we analyze sapronosis transmission, using the human pathogen Mycobacterium ulcerans that is responsible for Buruli ulcer. We show that the persistence of bacilli in aquatic ecosystems is driven by a seasonal upstream supply, and that the attachment and development of cells to aquatic living forms is essential for such pathogen persistence and population dynamics. Our work constitutes the first set of metacommunity models of sapronotic disease transmission, and is highly flexible for adaptation to other types of sapronosis. The importance of sapronotic agents on animal and human disease burden needs better understanding and new models of sapronosis disease ecology to guide the management and prevention of this important group of pathogens. Author summary: Bacterial pathogens responsible for sapronotic diseases represent a threat to public health, accounting for one-third of human infections. However, little is known about variations in infection risk in time and space, hence limiting control strategies development, due to a lack of research on these pathogens. In this study, we developed a first realistic mathematical model to describe the spatial and temporal dynamics of sapronotic bacteria and their interactions with wildlife in aquatic ecosystems. Our model allows identifying the characteristics of wildlife-sapronotic bacteria interactions that play the most important role in determining disease risks in animals and humans. [ABSTRACT FROM AUTHOR]

Reverse epidemiology is a mathematical modelling tool used to ascertain information about the source of a pathogen, given the spatial and temporal distribution of cases, hospitalisations and deaths. In the context of a deliberately released pathogen, such as Bacillus anthracis (the disease-causing organism of anthrax), this can allow responders to quickly identify the location and timing of the release, as well as other factors such as the strength of the release, and the realized wind speed and direction at release. These estimates can then be used to parameterise a predictive mechanistic model, allowing for estimation of the potential scale of the release, and to optimise the distribution of prophylaxis. In this paper we present two novel approaches to reverse epidemiology, and demonstrate their utility in responding to a simulated deliberate release of B. anthracis in ten locations in the UK and compare these to the standard grid-search approach. The two methods—a modified MCMC and a Recurrent Convolutional Neural Network—are able to identify the source location and timing of the release with significantly better accuracy compared to the grid-search approach. Further, the neural network method is able to do inference on new data significantly quicker than either the grid-search or novel MCMC methods, allowing for rapid deployment in time-sensitive outbreaks. Author summary: In this paper we demonstrate three methods for estimating the source location and timing of a deliberate release of Bacillus anthracis based on the temporal and spatial distribution of cases. Two of our proposed methods, a modified MCMC approach and a neural network based approach, provide significant improvements over previous methods by directly addressing the problematic parameter-likelihood surface, and, in the case of the neural network approach, addressing the slow deployment speeds of existing methods. Our results represent a major step forward in the accuracy and speed of epidemiological back-calculation. [ABSTRACT FROM AUTHOR]

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic. Author summary: During the recent COVID-19 pandemic, we all became familiar with the reproduction number, a crucial quantity to determine if the number of infections is going to increase or decrease. Understanding the past changes of this quantity is fundamental to produce realistic forecasts of the epidemic and to plan possible containment strategies. There are several methods to infer the values of the reproduction number and, thus, the number of new infections. Statistical methods are based on the analysis of the collected epidemiological data. Instead, modeling approaches (such as the popular SIR model) attempt constructing a set of mathematical equations whose solution aims at approximating the dynamics underlying the data. In this paper, we explore the use of a recently developed technique called Physics-Informed Neural Network, which tries to combine the two approaches and to simultaneously fit the data, infer the dynamics of the unknown parameters, and solve the model equations. The proposed PINN implementations are tested in different scenarios using both synthetic and real-world data referred to the COVID-19 pandemic outbreak in Italy. The promising results can pave the way for a wider use of PINNs in epidemiological applications. [ABSTRACT FROM AUTHOR]

The incidence of dengue virus disease has increased globally across the past half-century, with highest number of cases ever reported in 2019 and again in 2023. We analyzed climatological, epidemiological, and phylogenomic data to investigate drivers of two decades of dengue in Cambodia, an understudied endemic setting. Using epidemiological models fit to a 19-y dataset, we first demonstrate that climate-driven transmission alone is insufficient to explain three epidemics across the time series. We then use wavelet decomposition to highlight enhanced annual and multiannual synchronicity in dengue cycles between provinces in epidemic years, suggesting a role for climate in homogenizing dynamics across space and time. Assuming reported cases correspond to symptomatic secondary infections, we next use an age-structured catalytic model to estimate a declining force of infection for dengue through time, which elevates the mean age of reported cases in Cambodia. Reported cases in >70-y-old individuals in the 2019 epidemic are best explained when also allowing for waning multitypic immunity and repeat symptomatic infections in older patients. We support this work with phylogenetic analysis of 192 dengue virus (DENV) genomes that we sequenced between 2019 and 2022, which document emergence of DENV-2 Cosmopolitan Genotype-II into Cambodia. This lineage demonstrates phylogenetic homogeneity across wide geographic areas, consistent with invasion behavior and in contrast to high phylogenetic diversity exhibited by endemic DENV-1. Finally, we simulate an age-structured, mechanistic model of dengue dynamics to demonstrate how expansion of an antigenically distinct lineage that evades preexisting multitypic immunity effectively reproduces the older-age infections witnessed in our data. [ABSTRACT FROM AUTHOR]

Pathogen epidemics are key threats to human and wildlife health. Across systems, host protection from pathogens following initial exposure is often incomplete, resulting in recurrent epidemics through partially-immune hosts. Variation in population-level protection has important consequences for epidemic dynamics, but how acquired protection influences inter-individual heterogeneity in susceptibility and its epidemiological consequences remains understudied. We experimentally investigated whether prior exposure (none, low-dose, or high-dose) to a bacterial pathogen alters host heterogeneity in susceptibility among songbirds. Hosts with no prior pathogen exposure had little variation in protection, but heterogeneity in susceptibility was significantly augmented by prior pathogen exposure, with the highest variability detected in hosts given high-dose prior exposure. An epidemiological model parameterized with experimental data found that heterogeneity in susceptibility from prior exposure more than halved epidemic sizes compared with a homogeneous population with identical mean protection. However, because infection-induced mortality was also greatly reduced in hosts with prior pathogen exposure, reductions in epidemic size were smaller than expected in hosts with prior exposure. These results highlight the importance of variable protection from prior exposure and/or vaccination in driving population-level heterogeneity and epidemiological dynamics. Author summary: Individuals in a population are often highly variable in whether or not they get sick during an outbreak. This variability between individuals has important consequences for how widely a disease can spread. Therefore, it is useful to understand what drives the amount of variability in susceptibility present in populations as a whole. Because individuals in a population can have quite variable immune responses to the same type and dose of pathogen infection, one possibility is that populations of individuals with acquired immune protection from prior pathogen exposure are actually more variable in their susceptibility than populations of individuals with no previous pathogen infection. We tested this possibility using a songbird disease system as a model. We found that populations of birds for which we had generated immune protection by exposing them to a bacterial pathogen were far more variable in their susceptibility than birds that had never been infected before. We also show that this population-level variability in itself can strongly reduce the size of disease outbreaks. [ABSTRACT FROM AUTHOR]

This research delineates the advancement of a refined predictive algorithm centered on the Generalized Least Deviation Method (GLDM) specifically configured for analyzing COVID-19 infection trends in Dagestan using univariate time series data. Our methodology is characterized by its enhancement of forecast precision through diligent minimization of a bespoke loss function. The algorithm's innovation lies in its formulation, incorporating second-order relationships within the time series data: ...; where nj are the computed weights ascribed to historical data, and 3t denotes the error component. Our empirical analysis substantiates that by strategically accentuating pertinent coefficients and optimizing the loss function, there is a significant elevation in the model's forecasting accuracy. Consequently, the refined second-order GLDM model emerges as an advanced and applicable instrument for the prognostication of COVID-19 infection cases in Dagestan. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Innovations in aerobiological and epidemiological modeling are enabling the development of powerful techniques to infer connectivity networks for transboundary pathogens in ways that were not previously possible. The innovations are supported by improved access to historical and near real-time highly resolved weather data, multi-country disease surveillance data, and enhanced computing power. Using wheat rusts as an exemplar, we introduce a flexible modeling framework to identify characteristic pathways for long-distance spore dispersal within countries and beyond national borders. We show how the models are used for near real-time early warning systems to support smallholder farmers in East Africa and South Asia. Wheat rust pathogens are ideal exemplars because they continue to pose threats to food security, especially in regions of the world where resources for control are limited. The risks are exacerbated by the rapid appearance and spread of new pathogenic strains, prodigious spore production, and long-distance dispersal for transboundary and pandemic spread. [ABSTRACT FROM AUTHOR]

In this paper I apply the epidemiological model of the spread of beliefs and how they become cultural representations to the field of fallacies. The model suggests that beliefs tend to replicate as a virus does in a potential epidemic, and those strains that are dominant in a given socio-cultural sphere become cultural representations. My ultimate aim is to denounce the fact that some presumptive argumentation schemes are widely applied as definitive arguments, but turn out to be instances of common and traditional fallacies. Moreover, some such fallacies have managed to colonise the human mind and become cultural representations in society today. Adopting the approach I advocate here, we could say that the fallacy has become a belief, which has then managed to replicate like a virus, and finally the fallacy has become a cultural representation. One of the great harms that results from this process is that it is very difficult to open up effective lines of argument that expose the fallacious nature of these new and perverse cultural representations. [ABSTRACT FROM AUTHOR]

Background: Menopausal hormone therapy (MHT) can alleviate menopausal symptoms but has been associated with an increased risk of breast cancer. MHT prescription should be preceded by individualised risk/benefit evaluation; however, data outlining the impact of family history alongside different MHT therapeutic approaches are lacking. Aim: To quantify the risks associated with MHT use in women with varying breast cancer family histories of developing and dying from breast cancer. Design and setting: An epidemiological modelling study for women in England using the BOADICEA breast cancer prediction model and data relating to MHT use and breast cancer risk taken from research by the Collaborative Group on Hormonal Factors in Breast Cancer. Method: The risk of developing and dying from breast cancer between the ages of 50 and 80 years was modelled in women with four different breast cancer family history profiles: 'average', 'modest', 'intermediate', and 'strong' by using 1) background risks of breast cancer by age and family history, 2) relative risks for breast cancer associated with MHT use, and 3) 10-year breast cancer-specific net mortality rates. This study modelled use of combined oestrogen-progestogen MHT (cyclical or continuous) and oestrogen-only MHT. Results: For a woman of 'average' family history taking no MHT, the cumulative breast cancer risk (age 50–80 years) is 9.8%, and the risk of dying from the breast cancer is 1.7%. In this model, 5 years' exposure to combined-cyclical MHT (age 50–55 years) was calculated to increase these risks to 11.0% and 1.8%, respectively. For a woman with a 'strong' family history taking no MHT, the cumulative breast cancer risk is 19.6% (age 50–80 years), and the risk of dying from the breast cancer is 3.2%. With 5 years' exposure to MHT (age 50–55 years), this model showed that these risks increase to 22.4% and 3.5%, respectively. Conclusion: In this model, both family history and MHT are associated with increased risk of breast cancer. Estimates of the risks of breast cancer associated with MHT for women with different family histories can be used to support decision making around MHT prescription for women experiencing menopausal symptoms. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, over one thousand papers were published on "Susceptible- Exposed-Infectious-Removed" (SEIR) epidemic computational models. The English word "exposed" in its vernacular and public health usage means a state of having been in contact with an infectious individual, but not necessarily infected. In contrast, the term "exposed" in SEIR modeling usage typically stands for a state of already being infected but not yet being infectious to others, a state more properly termed "latently infected." In public health language, "exposed" means possibly infected, yet in SEIR modeling language, "exposed" means already infected. This paper retraces the conceptual and mathematical origins of this terminological disconnect and concludes that epidemic modelers should consider using the "SLIR" notational short-hand (L for Latent) instead of SEIR. [ABSTRACT FROM AUTHOR]

In this research, we introduce a comprehensive epidemiological model that accounts for multiple strains of an infectious disease and two distinct vaccination options. Vaccination stands out as the most effective means to prevent and manage infectious diseases. However, when there are various vaccines available, each with its costs and effectiveness, the decision-making process for individuals becomes paramount. Furthermore, the factor of waning immunity following vaccination also plays a significant role in influencing these choices. To understand how individuals make decisions in the context of multiple strains and waning immunity, we employ a behavioral model, allowing an epidemiological model to be coupled with the dynamics of a decision-making process. Individuals base their choice of vaccination on factors such as the total number of infected individuals and the cost-effectiveness of the vaccine. Our findings indicate that as waning immunity increases, people tend to prioritize vaccines with higher costs and greater efficacy. Moreover, when more contagious strains are present, the equilibrium in vaccine adoption is reached more rapidly. Finally, we delve into the social dilemma inherent in our model by quantifying the social efficiency deficit (SED) under various parameter combinations. [ABSTRACT FROM AUTHOR]

The basic reproduction number, R0, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating R0 from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition. We show that by conditioning a 'deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory. [ABSTRACT FROM AUTHOR]

Epidemiological compartmental models, such as SEIR (Susceptible, Exposed, Infectious, and Recovered) models, have been generally used in analyzing epidemiological data and forecasting the trajectory of transmission of infectious diseases such as COVID-19. Experience shows that accurately forecasting the trajectory of COVID-19 transmission curve is a big challenge for researchers in the field of epidemiological modeling because multiple unquantified factors can affect the trajectory of COVID-19 transmission. In the past years, we used a new compartmental model, l-i SEIR model, to analyze the COVID-19 transmission trend in the United States. Unlike the conventional SEIR model and the delayed SEIR model that use or partially use the approximation of temporal homogeneity, the l-i SEIR model takes into account chronological order of infected individuals in both latent (l) period and infectious (i) period, and thus improves the accuracy in forecasting the trajectory of transmission of infectious diseases, especially during periods of rapid rise or fall in the number of infections. This paper describes (1) how to use the new SEIR model (a mechanistic model) combined with fitting methods to simulate or predict trajectory of COVID-19 transmission, (2) how social interventions and new variants of COVID-19 significantly change COVID-19 transmission trends by changing transmission rate coefficient βn, the fraction of susceptible people (Sn/N), and the reinfection rate, (3) why accurately forecasting COVID-19 transmission trends is difficult, (4) what are the strategies that we have used to improve the forecast outcome and (5) what are some successful examples that we have obtained. [ABSTRACT FROM AUTHOR]

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. For R 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while for R 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios. [ABSTRACT FROM AUTHOR]

A useful parametric specification for the expected value of an epidemiological process is revived, and its statistical and empirical efficacy are explored. The Richards' curve is flexible enough to adapt to several growth phenomena, including recent epidemics and outbreaks. Here, two different estimation methods are described. The first, based on likelihood maximisation, is particularly useful when the outbreak is still ongoing and the main goal is to obtain sufficiently accurate estimates in negligible computational run-time. The second is fully Bayesian and allows for more ambitious modelling attempts such as the inclusion of spatial and temporal dependence, but it requires more data and computational resources. Regardless of the estimation approach, the Richards' specification properly characterises the main features of any growth process (e.g. growth rate, peak phase etc.), leading to a reasonable fit and providing good short- to medium-term predictions. To demonstrate such flexibility, we show different applications using publicly available data on recent epidemics where the data collection processes and transmission patterns are extremely heterogeneous, as well as benchmark datasets widely used in the literature as illustrative. [ABSTRACT FROM AUTHOR]

Simple Summary: The mortality of hepatocellular carcinoma (HCC) is rising globally, against the trend of other cancers. People with liver cirrhosis, even after hepatitis C treatment still face a high risk of HCC, requiring ongoing enrolment in HCC surveillance, and new technologies to improve diagnostic sensitivity are being explored. However, their impact on HCC survival remains uncertain relative to improving adherence to existing surveillance methods. This study uses mathematical modeling to assess how different strategies can reduce deaths from liver cancer in people with cirrhosis after being cured of hepatitis C. We compared the impact of improved adherence to ultrasound screening with increased HCC imaging sensitivity on HCC survival. Notably, we found that even modest enhancements in surveillance adherence (5–10 percentage point increases) exhibited significant survival benefits for people with hepatitis C-related cirrhosis, outperforming improvements in diagnostic sensitivity. Background & Aims: Hepatocellular carcinoma (HCC) presents a significant global health challenge, particularly among individuals with liver cirrhosis, with hepatitis C (HCV) a major cause. In people with HCV-related cirrhosis, an increased risk of HCC remains after cure. HCC surveillance with six monthly ultrasounds has been shown to improve survival. However, adherence to biannual screening is currently suboptimal. This study aimed to evaluate the effect of increased HCC surveillance uptake and improved ultrasound sensitivity on mortality among people with HCV-related cirrhosis post HCV cure. Methods: This study utilized mathematical modelling to assess HCC progression, surveillance, diagnosis, and treatment among individuals with cirrhosis who had successfully been treated for HCV. The deterministic compartmental model incorporated Barcelona Clinic Liver Cancer (BCLC) stages to simulate disease progression and diagnosis probabilities in 100 people with cirrhosis who had successfully been treated for hepatitis C over 10 years. Four interventions were modelled to assess their potential for improving life expectancy: realistic improvements to surveillance adherence, optimistic improvements to surveillance adherence, diagnosis sensitivity enhancements, and improved treatment efficacy Results: Realistic adherence improvements resulted in 9.8 (95% CI 7.9, 11.6) life years gained per cohort of 100 over a 10-year intervention period; 17.2 (13.9, 20.3) life years were achieved in optimistic adherence improvements. Diagnosis sensitivity improvements led to a 7.0 (3.6, 13.8) year gain in life years, and treatment improvements improved life years by 9.0 (7.5, 10.3) years. Conclusions: Regular HCC ultrasound surveillance remains crucial to reduce mortality among people with cured hepatitis C and cirrhosis. Our study highlights that even minor enhancements to adherence to ultrasound surveillance can significantly boost life expectancy across populations more effectively than strategies that increase surveillance sensitivity or treatment efficacy. [ABSTRACT FROM AUTHOR]

Fire blight disease, caused by Erwinia amylovora is present worldwide and affects over 40 countries in Europe where it is listed as a quarantine or regulated pest often due to ineffective control strategies maladapted to the respective production systems. In Portugal, the disease was confirmed in 2010 and the occurrence of disease outbreaks in new production areas has risen over the years. The disease affects the national production of apple and pear fruits, with greater impact on the national pear variety 'Rocha', widely exported to European countries and Brazil. The mild temperatures and high relative humidity promote the progression of the disease during winter, revealing the potential activity of the bacterium in the latency period (LP) of the host. Infection alert risk using the established predictive models Maryblight TM, Cougarblight and BIS98 was put in place in 2013 by Centro Operativo e Tecnológico Hortofrutícola Nacional (COTHN). These attempts to control the spread of this disease, showed low accuracy for the Portuguese epidemiological reality. Within the framework of project Fire4CAST we developed a new epidemiological model to predict fire blight disease using a systems biology approach integrating microbiological, cytological and genomic pathogen data with phenological host development and climatic variables. The presence of E. amylovora was monitored in orchards with fire blight history using standard laboratory tests. Simultaneously, the implementation of immune-flow cytometry (IFCM) highlighted the viability of E. amylovora populations prevailing during winter and early spring, long before bloom risk period. The integration of the whole data set allowed the development of the Fire4CAST predictive model, able to monitor the expected infection date (EID) and to define accurate outbreak alarms. Fire4CAST model enabled the detection of outbreak risk during winter based on rules that consider climatic data variables, which were validated by effective presence of live and active E. amylovora populations and real-time quantitative PCR (qPCR) data, accomplishing a precision rate of 83%. Field application of Fire4CAST can hopefully guide the implementation of successful control strategies, leading to more sustainable pome chain production areas. [ABSTRACT FROM AUTHOR]

This paper explores the application of complex network models and genetic algorithms in epidemiological modeling. By considering the small-world and Barabási–Albert network models, we aim to replicate the dynamics of disease spread in urban environments. This study emphasizes the importance of accurately mapping individual contacts and social networks to forecast disease progression. Using a genetic algorithm, we estimate the input parameters for network construction, thereby simulating disease transmission within these networks. Our results demonstrate the networks' resemblance to real social interactions, highlighting their potential in predicting disease spread. This study underscores the significance of complex network models and genetic algorithms in understanding and managing public health crises. [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. [ABSTRACT FROM AUTHOR]

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies. [ABSTRACT FROM AUTHOR]

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimalfinancial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional- –integral–-derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model. [ABSTRACT FROM AUTHOR]

An increasing number of disruptions in ports, plants and warehouses have generated ripple effects over supply networks impacting economic activity. We demonstrate how the spread of the pandemic geographically expands the ripple effect by reducing the workers’ participation in production, so undermining the ability of firms and, as a result, the entire cross-border sup- ply chain network to satisfy customers’ demands. Our model of the spatio-temporal dynamics of the propagation of Covid-19 infection for supply networks contributes toward ripple effect visualisation and quantification by combining the flow of goods and materials through a typical global supply chain with an epidemiological model. The model enables prospective analyses to be performed in what-if scenarios to simulate the impact on the workforce in each node. The outcome should be helpful tools for managers and scholars. Results from this research will help mitigate the impact and spread of a pandemic in a particular region and the ability of a supply network to overcome the ripple effect. A stylised case study of a cross-border supply chain illustrates the ripple effect by showing how waves with crests at varying dates impact the ability to serve demand showing how a supply chain manager can obtain a forward-looking picture. [ABSTRACT FROM AUTHOR]

Introduction: Depression during pregnancy can put strain on pregnant women's interpersonal relationships, the formation of emotional bonds with the fetus, and the adaptation to the new routine and social role post-pregnancy. Some studies have associated socioeconomic factors, emotional factors, interpersonal relationships, perceived social support, gestational risk, and the occurrence of certain diseases during pregnancy with higher risk of depression. Objectives: This study aimed to investigate the prevalence of depression during pregnancy and associated factors in low- and high-risk prenatal patients at a Brazilian university hospital. Methods: This study presents a retrospective and prospective cross-sectional design. A total of 684 prenatal psychological analysis records from a Brazilian tertiary university service were retrospectively evaluated to assess depression through the PRIME-MD questionnaire between 2002--2017. Between 2017 and 2018, 76 patients treated at the same service were prospectively evaluated with the aforementioned instrument. Medical records were accessed to obtain labor and birth data. Multivariate analyses assessed the association between sociodemographic, gestational or obstetric, and health variables and the presence of depression during pregnancy. Results: A total of 760 pregnant women were included in the study, with a depression prevalence of 20.66% (n = 157). At the time of assessment, 48 (21.05%) women from the low-risk pregnancy group and 109 (20.49%) from the high-risk pregnancy group were depressed. The mean age was 30.01 ± 6.55 years in the group with depression and 29.81 ± 6.50 years in the group without depression. In the univariate analysis, there was an association of risk for depression with absence of paid work, absence of a partner, low family income and diagnosis of epilepsy, being a protective factor the presence of diabetes during pregnancy. However, in the multivariate analysis, a lower family income, not having a partner at the time of the assessment, and the prevalence of epilepsy were independently associated with an increased risk of depression during pregnancy. Conclusion: This study showed that 1 in 5 women had depression during pregnancy, with no association with obstetric risk, but those women living in unfavorable economic conditions, without a partner, and having epilepsy were at increased risk of depression. [ABSTRACT FROM AUTHOR]

Emerging infectious diseases with zoonotic potential often have complex socioecological dynamics and limited ecological data, requiring integration of epidemiological modeling with surveillance. Although our understanding of SARS-CoV-2 has advanced considerably since its detection in late 2019, the factors influencing its introduction and transmission in wildlife hosts, particularly white-tailed deer (Odocoileus virginianus), remain poorly understood. We use a Susceptible-Infected-Recovered-Susceptible epidemiological model to investigate the spillover risk and transmission dynamics of SARS-CoV-2 in wild and captive white-tailed deer populations across various simulated scenarios. We found that captive scenarios pose a higher risk of SARS-CoV-2 introduction from humans into deer herds and subsequent transmission among deer, compared to wild herds. However, even in wild herds, the transmission risk is often substantial enough to sustain infections. Furthermore, we demonstrate that the strength of introduction from humans influences outbreak characteristics only to a certain extent. Transmission among deer was frequently sufficient for widespread outbreaks in deer populations, regardless of the initial level of introduction. We also explore the potential for fence line interactions between captive and wild deer to elevate outbreak metrics in wild herds that have the lowest risk of introduction and sustained transmission. Our results indicate that SARS-CoV-2 could be introduced and maintained in deer herds across a range of circumstances based on testing a range of introduction and transmission risks in various captive and wild scenarios. Our approach and findings will aid One Health strategies that mitigate persistent SARS-CoV-2 outbreaks in white-tailed deer populations and potential spillback to humans. Author summary: Novel zoonotic diseases persist and evolve in both human and non-human hosts, posing challenges for human and animal health. SARS-CoV-2, the virus responsible for the COVID-19 pandemic in humans, has been detected in white-tailed deer (Odocoileus virginianus) yet we have limited understanding of its introduction and transmission within deer populations. Here, we use epidemiological models to describe SARS-CoV-2 introduction and transmission patterns within wild and captive white-tailed deer populations. We found that captive deer herds faced a higher risk of spillover of SARS-CoV-2 from humans and higher transmission rate compared to wild deer. Despite these differences in wild and captive contexts, we found that transmission in both wild and captive contexts often resulted in persisting circulation of SARS-CoV-2. This circulation was determined by deer-deer transmission in both wild and captive contexts, rather than by high rates of introduction from humans. Outbreaks in wild populations were greater when these animals could interact with captive deer populations circulating SARS-CoV-2. SARS-CoV-2 appears to circulate in both captive and wild deer across a range of circumstances. Our findings help to inform how to best mitigate the introduction and spread of SARS-CoV-2 in deer, with benefits to protecting human health. [ABSTRACT FROM AUTHOR]

Mathematical modelling of a dengue epidemic with two serotypes including a temporary cross-immunity yields a nonlinear system consisting of ordinary differential equations (ODEs). We investigate an optimal control problem, where the integral of the infected humans is minimised within a time interval. The controls represent human actions to decrease the number of mosquitos in the model. An integral constraint is added, which takes a limitation on the sum of the human actions into account. On the one hand, we derive and apply a direct approach to solve the optimal control problem. Therein, a discretisation of the controls is constructed using spline interpolation in time. Consequently, a finite-dimensional constrained minimisation problem can be solved. On the other hand, we employ an indirect approach, where necessary conditions for an optimal solution are considered. This technique yields a multipoint boundary value problem of a larger system of ODEs including adjoint equations. We present results of numerical computations, where the two methods are compared. [ABSTRACT FROM AUTHOR]

We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations. [ABSTRACT FROM AUTHOR]

This paper shows how a new theory of epidemics can be developed for viral pandemics in a globally interconnected world. The study of the in-host dynamics and, in parallel, the spatial diffusion of epidemics defines the goal of our work, which looks ahead to new mathematical tools to model epidemics beyond the traditional approach of population dynamics. The approach takes into account the evolutionary nature of the virus, which can generate pseudo-Darwinian mutations and selection, while learning the presence of the virus and activating adaptive immunity. The study of immune competition plays a key role in both the in-host dynamics and the contagion dynamics. [ABSTRACT FROM AUTHOR]

Problem definition: The opioid epidemic is a crisis that has plagued the United States for decades. One central issue of the epidemic is inequitable access to treatment for opioid use disorder (OUD), which puts certain populations at a higher risk of opioid overdose. Methodology/results: We integrate a predictive dynamical model and a prescriptive optimization problem to compute high-quality opioid treatment facility and treatment budget allocations for each U.S. state. Our predictive model is a differential equation-based epidemiological model that captures the dynamics of the opioid epidemic. We use a process inspired by neural ordinary differential equations to fit this model to opioid epidemic data for each state and obtain estimates for unknown parameters in the model. We then incorporate this epidemiological model into a corresponding mixed-integer optimization problem (MIP) that aims to minimize the number of opioid overdose deaths and the number of people with OUD. We develop strong relaxations based on McCormick envelopes to efficiently compute approximate solutions to our MIPs that have a mean optimality gap of 3.99%. Our method provides socioeconomically equitable solutions, as it incentivizes investments in areas with higher social vulnerability (from the U.S. Centers for Disease Control's Social Vulnerability Index) and opioid prescribing rates. On average, when allowing for overbudget solutions, our approach decreases the number of people with OUD by 9.03±1.772% , increases the number of people in treatment by 88.75±26.223% , and decreases the number of opioid-related deaths by 0.58±0.111% after 2 years compared with the baseline epidemiological model's predictions. Managerial implications: Our solutions show that policymakers should target adding treatment facilities to counties that have significantly fewer facilities than their population share and are more socially vulnerable. Furthermore, we demonstrate that our optimization approach, guided by epidemiological and socioeconomic factors, should help inform these strategic decisions, as it yields population health benefits in comparison with benchmarks based solely on population and social vulnerability. History: This paper has been accepted in the Manufacturing & Service Operations Management Frontiers in Operations Initiative. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0042. [ABSTRACT FROM AUTHOR]

This article presents an agent-based simulation-optimization modeling and algorithmic framework to determine the optimal vaccine center location and vaccine allocation strategies under budget constraints during an epidemic outbreak. Both simulation and optimization models incorporate population health dynamics, such as susceptible (S), vaccinated (V), infected (I) and recovered (R), while their integrated utilization focuses on the COVID-19 vaccine allocation challenges. We first formulate a dynamic location–allocation Mixed-Integer Programming (MIP) model, which determines the optimal vaccination center locations and vaccines allocated to vaccination centers, pharmacies, and health centers in a multi-period setting in each region over a geographical location. We then extend the agent-based epidemiological simulation model of COVID-19 (Covasim) by adding new vaccination compartments representing people who take the first vaccine shot and the first two shots. The Covasim involves complex disease transmission contact networks, including households, schools, and workplaces, and demographics, such as age-based disease transmission parameters. We combine the extended Covasim with the vaccination center location-allocation MIP model into one single simulation-optimization framework, which works iteratively forward and backward in time to determine the optimal vaccine allocation under varying disease dynamics. The agent-based simulation captures the inherent uncertainty in disease progression and forecasts the refined number of susceptible individuals and infections for the current time period to be used as an input into the optimization. We calibrate, validate, and test our simulation-optimization vaccine allocation model using the COVID-19 data and vaccine distribution case study in New Jersey. The resulting insights support ongoing mass vaccination efforts to mitigate the impact of the pandemic on public health, while the simulation-optimization algorithmic framework could be generalized for other epidemics. [ABSTRACT FROM AUTHOR]

Per- and poly-fluoroalkylated substances (PFAS) are a large group of chemicals that persist both in the environment and in the body. Legacy PFAS, e.g., perfluorooctanoic acid and perfluorooctane sulfonic acid, are implicated as endocrine disruptors and reproductive and developmental toxicants in epidemiological and animal model studies. This review describes female reproductive outcomes of reported studies and includes where associative relationships between PFAS exposures and female reproductive outcomes have been observed as well as where those are absent. In animal models, studies in which PFAS are documented to cause toxicity and where effects are lacking are described. Discrepancies exist in both human and animal studies and are likely attributable to human geographical contamination, developmental status, duration of exposure, and PFAS chemical identity. Similarly, in animal investigations, the model used, exposure paradigm, and developmental status of the female are important and vary widely in documented studies. Taken together, support for PFAS as reproductive and developmental toxicants exists, although the disparity in study conditions and human exposures contribute to the variation in effects noted. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has presented a complex situation that requires a balance between control measures like lockdowns and easing restrictions. Control measures can limit the spread of the virus but can also cause economic and social issues. Easing restrictions can support economic recovery but may increase the risk of virus transmission. Mathematical approaches can help address these trade-offs by modeling the interactions between factors such as virus transmission rates, public health interventions, and economic and social impacts. A study using a susceptible-infected-susceptible (SIS) model with modified discrete time was conducted to determine the cost of handling COVID-19. The results showed that, without government intervention, the number of patients rejected by health facilities and the cost of handling a pandemic increased significantly. Lockdown intervention provided the least number of rejected patients compared to social distancing, but the costs of handling the pandemic in the lockdown scenario remained higher than those of social distancing. This research demonstrates that mathematical approaches can help identify critical junctures in a pandemic, such as limited health system capacity or high transmission rates, that require rapid response and appropriate action. By using mathematical analysis, decision-makers can develop more effective and responsive strategies, considering the various factors involved in the virus's spread and its impact on society and the economy. [ABSTRACT FROM AUTHOR]

The Caputo fractional-order differential operator is used in epidemiological models, but its accuracy benefits are typically ignored. We validated the suggested fractional epidemiological seasonal influenza model of the SVEIHR type to demonstrate the Caputo operator's relevance. We analysed the model using fractional calculus, revealing its basic properties and enhancing our understanding of disease progression. Furthermore, the positivity, bounds, and symmetry of the numerical scheme were examined. Adjusting the Caputo fractional-order parameter α = 0.99 provided the best fit for epidemiological data on infection rates. We compared the suggested model with the Caputo fractional-order system and the integer-order equivalent model. The fractional-order model had lower absolute mean errors, suggesting that it could better represent sickness transmission and development. The results underline the relevance of using the Caputo fractional-order operator to improve epidemiological models' precision and forecasting. Integrating fractional calculus within the framework of symmetry helps us build more reliable models that improve public health interventions and policies. [ABSTRACT FROM AUTHOR]

Parameter and initial conditions (factors) estimation is a challenging task in non-linear models. Even if researchers successfully estimate those model factors, they still should estimate their confidence intervals, which could require a high computational cost to turn them into informative values. Some methods in the literature attempt to estimate regions within the search space where factors may jointly exist and fit the experimental data, i.e., confidence contours. However, the estimation of such confidence contours comes up with several issues as the number of factors increases. In this work we propose a method to compute a region within the confidence contour of an inverse problem, we denote this region as the confidence sub-contour box (CSB). To estimate a CSB of an inverse problem, we propose two main algorithms alongside their interpretation and validation, testing their performance with two epidemiological models for different diseases and different kinds of data. Moreover, we exposed some desirable properties of the method through numerical experiments, such as user-defined uncertainty level, asymmetry of the resultant intervals regarding the nominal value, sensitivity assessment related to the interval length for each factor, and identification of true-influential factors. We set available all the algorithms we used in this paper at Mathworks in the GSUA-CSB toolbox. [ABSTRACT FROM AUTHOR]

The focus of this paper is to investigate the exact solutions of a diffusive susceptible‐infectious‐recovered (SIR) epidemic model, characterized by a nonlinear incidence. A four‐dimensional Lie point symmetry algebra is obtained for this model. We utilize the Lie symmetries to deduce the optimal system of one‐dimensional subalgebras. The reductions and group‐invariant solutions are obtained with the aid of these subalgebras. We also derive new group‐invariant solutions and reductions for the underlying model via subalgebras that are related to the optimal system by adjoint maps. We developed the diffusive susceptible‐infectious‐quarantined (SIQ) model with quarantine‐adjusted incidence function to understand the transmission dynamics of COVID‐19. [ABSTRACT FROM AUTHOR]

Most fine ambient particulate matter (PM2.5)-based epidemiological models use globalized concentration-response (CR) functions assuming that the toxicity of PM2.5 is solely mass-dependent without considering its chemical composition. Although oxidative potential (OP) has emerged as an alternate metric of PM2.5 toxicity, the association between PM2.5 mass and OP on a large spatial extent has not been investigated. In this study, we evaluate this relationship using 385 PM2.5 samples collected from 14 different sites across 4 different continents and using 5 different OP (and cytotoxicity) endpoints. Our results show that the relationship between PM2.5 mass vs. OP (and cytotoxicity) is largely non-linear due to significant differences in the intrinsic toxicity, resulting from a spatially heterogeneous chemical composition of PM2.5. These results emphasize the need to develop localized CR functions incorporating other measures of PM2.5 properties (e.g., OP) to better predict the PM2.5-attributed health burdens. This study shows that the relationship between concentrations of ambient fine particulate matter (PM2.5) and its health effects may vary in different regions of the world due to significant spatial variations in the toxicities of PM2.5. [ABSTRACT FROM AUTHOR]

In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B ′ / B = F ⊕ − F ⊖ , where F ⊖ represents a reaction factor reflecting the stress proportional to the active group's percentage variation. Conversely, F ⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F ⊕ = 0 , we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model's behavior and its implications for understanding disease transmission. [ABSTRACT FROM AUTHOR]

The object of the study is epidemiological grouping using the SEIR mathematical model on a machine learning-based multilayer network. The problems in this research are related to managing epidemiological data on a large scale to determine disease patterns and identification such as the number of recovered cases, number of infected cases and number of deaths and demographic factors. In the process, traditional methods make it difficult to carry out processes such as determining patterns and identifying diseases. So, it is necessary to use machine learning and the SEIR (Susceptible-Exposed-Infectious-Recovered) mathematical model which can be integrated with multilayer networks to increase accuracy and effectiveness in identifying diseases and determining patterns. The results obtained from this research are a model that can identify and determine patterns of disease spread in largescale epidemiological data. In its application, the SEIR mathematical model combined into a social layer and an environmental layer in a multilayer network. This research is research with a level of novelty in the application of the SEIR mathematical model to multilayer networks and machine learning so that the model formed can be used to view the distribution of epidemiological data for disease-related information. Machine learning aims to process large-scale data in minimal time resulting in clustering and identification of diseases such as flu, Covid-19 and pneumonia. This research has an accuracy of 94 % using the MAPE evaluation technique. It is hoped that the resulting model can be used in the world of health for disease mapping in certain areas as a reference for mitigating the spread of disease. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model's equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of compatimental epidemiological models consisting of Susceptible, Infected, and Removed (SIR) individuals with a perturbation factor or exterior effects such as noise, climate change, pollution, etc. We prove the existence and uniqueness of a limit cycle confined in a nonempty closed and convex set by relying on a recent result of Lobanova and Sadovskii. Moreover, we study the existence of Hopf and Bogdanov-Takens bifurcations by applying respectively Poincare-Andronov-Hopf bifurcation theorem and Bogdanov-Takens theorem. Eventually, using Scilab, we illustrate the validity of our results with numerical simulations and also interpret them. [ABSTRACT FROM AUTHOR]