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Across the world, the officially reported number of COVID-19 deaths is likely an undercount. Establishing true mortality is key to improving data transparency and strengthening public health systems to tackle future disease outbreaks. In this study, we estimated excess deaths during the COVID-19 pandemic in the Pune region of India. Excess deaths are defined as the number of additional deaths relative to those expected from pre-COVID-19-pandemic trends. We integrated data from: (a) epidemiological modeling using pre-pandemic all-cause mortality data, (b) discrepancies between media-reported death compensation claims and official reported mortality, and (c) the wisdom of crowds public surveying. Our results point to an estimated 14,770 excess deaths [95% CI 9820-22,790] in Pune from March 2020 to December 2021, of which 9093 were officially counted as COVID-19 deaths. We further calculated the undercount factor-the ratio of excess deaths to officially reported COVID-19 deaths. Our results point to an estimated undercount factor of 1.6 [95% CI 1.1-2.5]. Besides providing similar conclusions about excess deaths estimates across different methods, our study demonstrates the utility of frugal methods such as the analysis of death compensation claims and the wisdom of crowds in estimating excess mortality.

The dynamics of the propagation and outspread of infectious diseases are eminently intricate, mainly due to the heterogeneity of the host individuals. In this paper, an age‐stratified SEIR (susceptible‐exposed‐infected‐recovered) epidemiological model incorporating saturated treatment function and heterogeneous contact rates is developed to study infectious disease transmission dynamics among various age groups. The expression for the basic reproduction number R0$$ {R}_0 $$ and conditions for the global stability of the system have been derived by a recently developed graph‐theoretic (GT) approach. Digraph reduction creates a GT version of the Gauss elimination method for computing the R0$$ {R}_0 $$. The global dynamics results have been formed by constructing the Lyapunov function using a GT approach. The endemic equilibrium exists uniquely if R0>1$$ {R}_0>1 $$, whereas the disease‐free equilibrium is observed to be globally stable if R0≤1$$ {R}_0\le 1 $$. The numerical simulations are demonstrated by extracting the daily reported COVID‐19 cases for the second wave in Italy. The age‐dependent contact matrix for the Republic of Italy (data sourced from the POLYMOD study) is computed via paper–diary methodology (PDM) grounded on a population‐prospective survey in European countries. Our numerical findings imply that (i) for the age group (20–49) years and (50–69) years, the number of infected persons is quite double as compared with the exposed cases; (ii) approximately 50% of positive cases lies in (20–69) years age group; (iii) for the (00–19) years age group, only half of the exposed individuals got infected; and (iv) a consistent graph is detected for the age group of (70–99) years in both cases; it shows that almost all the exposed got infected. [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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Outbreak response to quarantine pathogens and pests in the European Union (EU) is regulated by the EU Plant Health Law, but the performance of outbreak management plans in terms of their effectiveness and efficiency has been quantified only to a limited extent. As a case study, the disease dynamics of almond leal' scorch, caused by Xylella fastidiosa, in the affected area of Alicante, Spain, were approximated using an individual-based spatial epidemiological model. The emergence of this outbreak was dated based on phylogenetic studies, and official surveys were used to delimit the current extent of thé disease. Different survey strategies and disease control measures were compared to determine their effectiveness and efficiency for outbreak management in relation to a baseline scenario without interventions. One-step and two-step survey approaches were compared with different confidence levels, buffer zone sizes, and eradication radii, including those set by the EU legislation for X. fastidiosa. The effect of disease control interventions was also considered by decreasing the transmission rate in the buffer zone. All outbreak management plans reduced the number of infected trees (effectiveness), but large differences were observed in the number of susceptible trees not eradicated (efficiency). The two-step survey approach, high confidence level, and the reduction in lhe transmission rate increased the efficiency. Only the outbreak management plans with the two-step survey approach removed infected trees completely, but they required greater survey efforts. Although control measures reduced disease spread, surveillance was the key factor in the effectiveness and efficiency of the outbreak management plans. [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]

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]

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]

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]

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]

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]

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]

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]

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]

A challenging SIR epidemiological dynamic model with harmonic rate of incidence and nonlinear rate of recovery is developed to examine the effects of available beds in hospitals and intervention decrease upon the propagation of viral disease. The incorporation of the harmonic mean as an incidence rate is the novelty of the present manuscript. The assumed incidence rate is less sensitive to the larger values of the variables and proves more advantageous for highly skewed data compared to the bi-linear and monod types of incidence rates. For model's stability, precise mathematical conclusions have been produced. The model has two states of equilibrium: an infection-free equilibrium (E 0) , whenever the threshold number assumes values less than one, and a disease-present state (E 1) , whenever R 0 > 1. We employ the principle of LaSalle invariance and Lyapunov's direct technique to demonstrate that the basic threshold quantity R 0 < 1 indicates the global asymptotic stability of E 0. Also whenever 1 < R 0 then the equilibrium point E 1 is stable, under specific parametric conditions. The optimal control strategies for the described model are chosen with the aid of maximum principle of Pontryagin. To support the analytical conclusions, some numerical results are presented. The study's findings show that the model can accurately reflect the complex dynamics of numerous epidemic diseases, resulting in a considerable decrease in infection transmission. [ABSTRACT FROM AUTHOR]

Background Distributed lag non-linear models (DLNMs) are the reference framework for modelling lagged non-linear associations. They are usually used in large-scale multi-location studies. Attempts to study these associations in small areas either did not include the lagged non-linear effects, did not allow for geographically-varying risks or downscaled risks from larger spatial units through socioeconomic and physical meta-predictors when the estimation of the risks was not feasible due to low statistical power. Methods Here we proposed spatial Bayesian DLNMs (SB-DLNMs) as a new framework for the estimation of reliable small-area lagged non-linear associations, and demonstrated the methodology for the case study of the temperature-mortality relationship in the 73 neighbourhoods of the city of Barcelona. We generalized location-independent DLNMs to the Bayesian framework (B-DLNMs), and extended them to SB-DLNMs by incorporating spatial models in a single-stage approach that accounts for the spatial dependence between risks. Results The results of the case study highlighted the benefits of incorporating the spatial component for small-area analysis. Estimates obtained from independent B-DLNMs were unstable and unreliable, particularly in neighbourhoods with very low numbers of deaths. SB-DLNMs addressed these instabilities by incorporating spatial dependencies, resulting in more plausible and coherent estimates and revealing hidden spatial patterns. In addition, the Bayesian framework enriches the range of estimates and tests that can be used in both large- and small-area studies. Conclusions SB-DLNMs account for spatial structures in the risk associations across small areas. By modelling spatial differences, SB-DLNMs facilitate the direct estimation of non-linear exposure-response lagged associations at the small-area level, even in areas with as few as 19 deaths. The manuscript includes an illustrative code to reproduce the results, and to facilitate the implementation of other case studies by other researchers. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when Δ < 0 ( Δ appears in Section 3), the three classes I t , M t , and R t appearing in the model go extinct at an exponential rate, and the susceptible class S t almost surely converges to the solution of the boundary equation exponentially. When Δ > 0 , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of Δ = 0 under some conditions. Some examples were listed to confirm the obtained results. The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when ( appears in Section 3), the three classes , , and appearing in the model go extinct at an exponential rate, and the susceptible class almost surely converges to the solution of the boundary equation exponentially. When , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of under some conditions. Some examples were listed to confirm the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a generalized mosquito-borne epidemic model with a general nonlinear incidence rate, which was studied from both deterministic and stochastic insights. In the deterministic model, we proved that the endemic equilibrium was globally asymptotically stable when the basic reproduction number R 0 was greater than unity and the disease free equilibrium was globally asymptotically stable when R 0 was lower than unity. In addition, considering the effect of environmental noise on the spread of infectious diseases, we developed a stochastic model in which the infection rates were assumed to satisfy the mean-reverting log-normal Ornstein-Uhlenbeck process. For this stochastic model, two critical values, known as R 0 s and R 0 E , were introduced to determine whether the disease will persist or die out. Additionally, the exact probability density function of the stationary distribution near the quasi-equilibrium point was obtained. Numerical simulations were conducted to validate the results obtained and to examine the impact of stochastic perturbations on the model. In this paper, we proposed a generalized mosquito-borne epidemic model with a general nonlinear incidence rate, which was studied from both deterministic and stochastic insights. In the deterministic model, we proved that the endemic equilibrium was globally asymptotically stable when the basic reproduction number was greater than unity and the disease free equilibrium was globally asymptotically stable when was lower than unity. In addition, considering the effect of environmental noise on the spread of infectious diseases, we developed a stochastic model in which the infection rates were assumed to satisfy the mean-reverting log-normal Ornstein-Uhlenbeck process. For this stochastic model, two critical values, known as and , were introduced to determine whether the disease will persist or die out. Additionally, the exact probability density function of the stationary distribution near the quasi-equilibrium point was obtained. Numerical simulations were conducted to validate the results obtained and to examine the impact of stochastic perturbations on the model. [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]

The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant, host, and non-pharmaceutical interventions (NPIs). All reported cases in the Putian epidemic (September 8–October 2, 2021, Delta variant B.1.617.2) and Fuzhou epidemic (October 22–November 18, 2022, Omicron variant BA.5.2) were classified by sex, age group, occupation, and location in this study. Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention, we established a virus-oriented SVEIR (Susceptible–Vaccinated–Exposed–Infected–Recovered) model to investigate the dynamic evolution features of these two variants and the effects of NPIs. The optimal simulations were carried out with variants and scenario investigations. The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19, and that the Omicron variant was more infectious than the Delta variant. Moreover, the dynamic investigations revealed the increasing tendencies from Delta to Omicron, such as the basic reproduction number, infection rate, percentage of high-risk cases, and the growth rate. Decreasing tendencies were also identified, such as the average recovery period, the awareness delay, and the percentage of symptomatic cases. This study highlighted that NPIs played critical roles in successfully containing the two epidemics. Such interventions are strongly recommended to public health policymakers. [ABSTRACT FROM AUTHOR]

Mathematical models highlighted the importance of pathogen‐mediated invasion, with the replacement of red squirrels by squirrelpox virus (SQPV) carrying grey squirrels in the UK, a well‐known example.In this study, we combine new epidemiological models, with a range of infection characteristics, with recent longitudinal field and experimental studies on the SQPV dynamics in red and grey squirrel populations to better infer the mechanistic basis of the disease interaction.A key finding is that a model with either partial immunity or waning immunity and reinfection, where individuals become seropositive on the second exposure to infection, that up to now has been shown in experimental data only, can capture the key aspects of the field study observations.By fitting to SQPV epidemic observations in isolated red squirrel populations, we can infer that SQPV transmission between red squirrels is significantly (4×) higher than the transmission between grey squirrels and as a result our model shows that disease‐mediated replacement of red squirrels by greys is considerably more rapid than replacement in the absence of SQPV.Our findings recover the key results of the previous model studies, which highlights the value of simple strategic models that are appropriate when there are limited data, but also emphasise the likely complexity of immune interactions in wildlife disease and how models can help infer disease processes from field data. [ABSTRACT FROM AUTHOR]

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. In the first part of this paper, we propose two new compartmental epidemiological models and study their equilibria, obtaining an endemic threshold theorem for the first model. In the second part of the paper, we treat the second model as an affine control system with two controls: vaccination and mitigation. We show that this system is static feedback linearizable, presents some simulations, and investigates an optimal control version of the problem. We conclude with some open problems and ideas for future research. [ABSTRACT FROM AUTHOR]

Superspreading events underscore the uneven distribution of COVID-19 transmission among individuals and locations. These heterogenous transmission patterns could stem from human mobility, yet the underlying mechanisms are still not fully understood. Here, we employ an agent-based model incorporating urban scaling structure to simulate fine-grained mobility and the human-to-human transmission process. Our results reveal that not only the quantity but also the scaling structure of mobility profoundly influences local transmission risk. Urban scaling structure is characterized by a widely found power-law scaling distribution of mobility volumes across different locations. By integrating this structure, our model fits reasonably well with empirical Omicron data at various spatial scales in Hong Kong. Further analyses show a positive association between the scaling index, representing the location's importance within the structure, and local transmission risks among urban areas as well as the likelihood of becoming superspreaders among local visitors. This implies that urban scaling structure could offer the first-mover advantage to a minority of places and individuals to infect earlier and thus infect more. This study brings important insights for the transmission dynamics of COVID-19 and similar diseases, highlighting the role of urban scaling structure in influencing local transmission risks and superspreading events. [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 centers on an eco-epidemiological predator-prey model that accounts for hunting cooperation among predators and prey shelter and fear in afflicted prey. The objective is to investigate the effects of parameter factors on the model's bifurcation behavior. Theoretical part of this study demonstrate that a transcritical bifurcation can result from infection rate and refuge rate. Furthermore, fear rate can cause a Hopf-bifurcation to arise close to the positive equilibrium point. The presence of local bifurcations close to the non-trivial equilibrium points is verified by numerical analysis, which also guarantees the veracity of the theoretical results. [ABSTRACT FROM AUTHOR]

This research paper aims to study the impact of COVID-19 on the economy, where we have extended the standard epidemiological model, the Susceptible–Infected–Recovered (SIR) model. In the economy's dynamics, we have incorporated aggregate demand and aggregate supply and further set up a system of three-dimensional nonlinear differential equations, which is more likely the Labor–Infected–Quarantine (LIQ) model, an extension of the SIR model. Here, we have derived the steady-state condition and analyzed the model's stability. In addition, we have done a comparative static analysis of parameters with some policy implications. We aim to achieve the twin objective, i.e., controlling the pandemic and reviving the economy under the set of the policy mix. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive exploration of physics-informed neural networks and their core features. It delves into their role in tackling inverse problems inherent in ordinary differential equation-based models. Within this context, we introduce a two-group epidemiological model, elucidating its fundamental attributes. The central objective of this research is to accurately estimate the model parameters for both groups in the epidemiological model. We offer a detailed exposition of the adopted methodology, providing insights into the algorithm and the techniques employed for its implementation. Through this analysis, we illuminate the complexities of our study, contributing to the growing body of knowledge in this field, which intersects epidemiology and neural network-based parameter estimation for an enriched understanding of infectious disease dynamics. [ABSTRACT FROM AUTHOR]