Bifurcation and optimal control for an infectious disease model with the impact of information

A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper,and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is considered.First,we perform the analysis for the existence of equilibria and the stability properties of the proposed model.In particular,the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium Ee when the basic reproduction number Ro>1.Second,mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around Ee.Third,based on the numerical results,it is shown that the information coverage and the average information delay may lead to more complex dynamical behaviors.Finally,the optimal control problem is established with information-infuenced vaccination and treatment as control variables.The corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle,and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments.

The collaboration between infectious disease modeling and public health decision-making based on the COVID-19

Public health decision-making may have great uncertainty especially in dealing with emerging infectious diseases,so it is necessary to establish a collaborative mechanism among modelers,epidemiologists,and public health decision-makers to reduce the uncertainty as much as possible.We searched the relevant studies on transmission dynamics modeling of infectious diseases,SARS,MERS,and COVID-19 as of March 1,2021 based on PubMed.We compared the key health decision-making time points of SARS,MERS,and COVID-19 prevention and control,and the publication time points of modeling research,to reveal the collaboration between infectious disease modeling and public health decision-making in the context of the COVID-19 pandemic.Searching with infectious disease and mathematical model as keywords,there were 166,81 and 1289 studies on the modeling of infectious disease transmission dynamics of SARS,MERS,and COVID-19 were retrieved respectively.Based on the modeling application framework of public health practice proposed in the current study,the collaboration among modelers,epidemiologists and public health decision-makers should be strengthened in the future.

Numerical Simulation and Parameter Estimation of Fractional-Order Dynamic Epidemic Model for COVID-19

The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.

Establishment of a Fractional Order COVID-19 Model and Its Feasibility Analysis

This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.

Call for papers of the special issue on Animal Models and Infectious Diseases

Primates and animal models are major areas of coverage for Zoological Research （ZR）. Over the past few years, ZR has released a series of special issues/topics addressing various aspects of these areas, e.g., ge- netics, immunology, and physiology neuroscience. A special issue for 2017 focusing on ＂Animal Models of Infectious Diseases＂ is under preparation and, so far, includes original research articles and reviews on filo- viruses and coxsackievirus involving guinea pigs, mice, and other species. Further to this, ZR would like to extend a very warm invitation to all peer researchers in the field to submit outstanding work to the journal on this special issue.

Big data technology in infectious diseases modeling,simulation,and prediction after the COVID-19 outbreak

After the outbreak of COVID-19,the interaction of infectious disease systems and social systems has challenged traditional infectious disease modeling methods.Starting from the research purpose and data,researchers im-proved the structure and data of the compartment model or used agents and artificial intelligence based models to solve epidemiological problems.In terms of modeling methods,the researchers use compartment subdivi-sion,dynamic parameters,agent-based model methods,and artificial intelligence related methods.In terms of factors studied,the researchers studied 6 categories:human mobility,nonpharmaceutical interventions(NPIs),ages,medical resources,human response,and vaccine.The researchers completed the study of factors through modeling methods to quantitatively analyze the impact of social systems and put forward their suggestions for the future transmission status of infectious diseases and prevention and control strategies.This review started with a research structure of research purpose,factor,data,model,and conclusion.Focusing on the post-COVID-19 infectious disease prediction simulation research,this study summarized various improvement methods and analyzes matching improvements for various specific research purposes.

Global Stability of SEIRS Model in Epidemiology

In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.

A generalized differential equation compartmental model of infectious disease transmission

For decades,mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression,control,and prevention of disease spread.Of these models,one of the most fundamental is the SIR differential equation model.However,this ubiquitous model has one significant and rarely acknowledged shortcoming:it is unable to account for a disease's true infectious period distribution.As the misspecification of such a biological characteristic is known to significantly affect model behavior,there is a need to develop new modeling approaches that capture such information.Therefore,we illustrate an innovative take on compartmental models,derived from their general formulation as systems of nonlinear Volterra integral equations,to capture a broader range of infectious period distributions,yet maintain the desirable formulation as systems of differential equations.Our work illustrates a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations,instead of the typical inflated model sizes required by traditional differential equation compartmental models,and a compartmental model that captures any mean,standard deviation,skewness,and kurtosis of an infectious period distribution with 4 differential equations.The significance of our work is that it opens up a new class of easyto-use compartmental models to predict disease outbreaks that do not require a complete overhaul of existing theory,and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics,public health,and evolutionary biology.

Understanding the impact of HIV on mpox transmission in the MSM population: A mathematical modeling study

The recent mpox outbreak(in 2022e2023)has different clinical and epidemiological features compared with previous outbreaks of the disease.During this outbreak,sexual contact was believed to be the primary transmission route of the disease.In addition,the community of men having sex with men(MSM)was disproportionately affected by the outbreak.This population is also disproportionately affected by HIV infection.Given that both diseases can be transmitted sexually,the endemicity of HIV,and the high sexual behavior associated with the MSM community,it is essential to understand the effect of the two diseases spreading simultaneously in an MSM population.Particularly,we aim to understand the potential effects of HIV on an mpox outbreak in the MSM population.We develop a mechanistic mathematical model of HIV and mpox co-infection.Our model incorporates the dynamics of both diseases and considers HIV treatment with antiretroviral therapy(ART).In addition,we consider a potential scenario where HIV infection increases susceptibility to mpox,and investigate the potential impact of this mechanism on mpox dynamics.Our analysis shows that HIV can facilitate the spread of mpox in an MSM population,and that HIV treatment with ART may not be sufficient to control the spread of mpox in the population.However,we showed that a moderate use of condoms or reduction in sexual contact in the population combined with ART is beneficial in controlling mpox transmission.Based on our analysis,it is evident that effective control of HIV,specifically through substantial ART use,moderate condom compliance,and reduction in sexual contact,is imperative for curtailing the transmission of mpox in an MSM population and mitigating the compounding impact of these intertwined epidemics.

A primer on multiscale modelling of infectious disease systems

The development of multiscale models of infectious disease systems is a scientific endeavour whose progress depends on advances on three main frontiers:(a)the conceptual framework frontier,(b)the mathematical technology or technical frontier,and(c)the scientific applications frontier.The objective of this primer is to introduce foundational concepts in multiscale modelling of infectious disease systems focused on these three main frontiers.On the conceptual framework frontier we propose a three-level hierarchical framework as a foundational idea which enables the discussion of the structure of multiscale models of infectious disease systems in a general way.On the scientific applications frontier we suggest ways in which the different structures of multiscale models can serve as infrastructure to provide new knowledge on the control,elimination and even eradication of infectious disease systems,while on the mathematical technology or technical frontier we present some challenges that modelers face in developing appropriate multiscale models of infectious disease systems.We anticipate that the foundational concepts presented in this primer will be central in articulating an integrated and more refined disease control theory based on multiscale modelling-the all-encompassing quantitative representation of an infectious disease system.

Modeling the role of public health education in Ebola virus disease outbreaks in Sudan

Public involvement in Ebola Virus Disease(EVD)prevention efforts is key to reducing disease outbreaks.Targeted education through practical health information to particular groups and sub-populations is crucial to controlling the disease.In this paper,we study the dynamics of Ebola virus disease in the presence of public health education with the aim of assessing the role of behavior change induced by health education to the dynamics of an outbreak.The power of behavior change is evident in two outbreaks of EVD that took place in Sudan only 3 years apart.The first occurrence was the first documented outbreak of EVD and produced a significant number of infections.The second outbreak produced far fewer cases,presumably because the population in the region learned from the first outbreak.We derive a system of ordinary differential equations to model these two contrasting behaviors.Since the population in Sudan learned from the first outbreak of EVD and changed their behavior prior to the second outbreak,we use data from these two instances of EVD to estimate parameters relevant to two contrasting behaviors.We then simulate a future outbreak of EVD in Sudan using our model that contains two susceptible populations,one being more informed about EVD.Our finding show how a more educated population results in fewer cases of EVD and highlights the importance of ongoing public health education.

The transmission mechanism theory of disease dynamics:Its aims,assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process.Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history,dating back to over a century now,that knowledge has not yet been formalized into a scientific theory.In this article,we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system,disease dynamics is determined by transmission as the main dynamic disease process.Therefore,the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now.The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims,assumptions and limitations.

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.

Time-varying and state-dependent recovery rates in epidemiological models

Differential equation models of infectious disease have undergone many theoretical extensions that are invaluable for the evaluation of disease spread.For instance,while one traditionally uses a bilinear term to describe the incidence rate of infection,physically more realistic generalizations exist to account for effects such as the saturation of infection.However,such theoretical extensions of recovery rates in differential equation models have only started to be developed.This is despite the fact that a constant rate often does not provide a good description of the dynamics of recovery and that the recovery rate is arguably as important as the incidence rate in governing the dynamics of a system.We provide a first-principles derivation of state-dependent and time-varying recovery rates in differential equation models of infectious disease.Through this derivation,we demonstrate how to obtain time-varying and state-dependent recovery rates based on the family of Pearson distributions and a power-law distribution,respectively.For recovery rates based on the family of Pearson distributions,we show that uncertainty in skewness,in comparison to other statistical moments,is at least two times more impactful on the sensitivity of predicting an epidemic's peak.In addition,using recovery rates based on a power-law distribution,we provide a procedure to obtain state-dependent recovery rates.For such state-dependent rates,we derive a natural connection between recovery rate parameters with the mean and standard deviation of a power-law distribution,illustrating the impact that standard deviation has on the shape of an epidemic wave.

Assessing the future progression of COVID-19 in Iran and its neighbors using Bayesian models

Background:The short term forecasts regarding different parameters of the COVID-19 are very important to make informed decisions.However,majority of the earlier contributions have used classical time series models,such as auto regressive integrated moving average(ARIMA)models,to obtain the said forecasts for Iran and its neighbors.In addition,the impacts of lifting the lockdowns in the said countries have not been studied.The aim of this paper is to propose more flexible Bayesian structural time series(BSTS)models for forecasting the future trends of the COVID-19 in Iran and its neighbors,and to compare the predictive power of the BSTS models with frequently used ARIMA models.The paper also aims to investigate the casual impacts of lifting the lockdown in the targeted countries using proposed models.Methods:We have proposed BSTS models to forecast the patterns of this pandemic in Iran and its neighbors.The predictive power of the proposed models has been compared with ARIMA models using different forecast accuracy criteria.We have also studied the causal impacts of resuming commercial/social activities in these countries using intervention analysis under BSTS models.The forecasts for next thirty days were obtained by using the data from March 16 to July 22,2020.These data have been obtained from Our World in Data and Humanitarian Data Exchange(HDX).All the numerical results have been obtained using R software.Results:Different measures of forecast accuracy advocated that forecasts under BSTS models were better than those under ARIMA models.Our forecasts suggested that the active numbers of cases are expected to decrease in Iran and its neighbors,except Afghanistan.However,the death toll is expected to increase at more pace in majority of these countries.The resuming of commercial/social activities in these countries has accelerated the surges in number of positive cases.Conclusions:The serious efforts would be needed to make sure that these expected figures regarding active number of cases come true.Iran and its neighbors need to improve their extensive healthcare infrastructure to cut down the higher expected death toll.Finally,these countries should develop and implement the strict SOPs for the commercial activities in order to prevent the expected second wave of the pandemic.

Forecasting the spread of the COVID-19 pandemic in Kenya using SEIR and ARIMA models

COVID-19,a coronavirus disease 2019,is an ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2(SARS-CoV-2).The first case in Kenya was identified on March 13,2020,with the pandemic increasing to about 237,000 confirmed cases and 4,746 deaths by August 2021.We developed an SEIR model forecasting the COVID-19 pandemic in Kenya using an Autoregressive Integrated moving averages(ARIMA)model.The average time difference between the peaks of wave 1 to wave 4 was observed to be about 130 days.The 4th wave was observed to have had the least number of daily cases at the peak.According to the forecasts made for the next 60 days,the pandemic is expected to continue for a while.The 4th wave peaked on August 26,2021(498th day).By October 26,2021(60th day),the average number of daily infections will be 454 new cases and 40 severe cases,which would require hospitalization,and 16 critically ill cases requiring intensive care unit services.The findings of this study are key in developing informed mitigation strategies to ensure that the pandemic is contained and inform the preparedness of policymakers and health care workers.

Dynamics of an SIRS model with age structure and two delays

ln this paper,we propose and investigate an SlRS model with age structure and twodelays.Both the infected and the recovered individuals have age structure,the infectionrate(from the infective to the susceptible)and the immune loss rate(from the recoveredto the susceptible)are related to two independent time delays,respectively.We provethat the proposed age structured SIRS model is well-posed by using the Co-semigrouptheory.The basic reproduction number Ro is given,and the unique endemic equilib-rium exists when R_(0)>1,while the disease-free equilibrium always exists.A rigorousmathematical analysis for the stability of two equilibria is provided.The disease-freeequilibrium is local asymptotically stable if R_(0)<1,and the endemic equilibrium is localasymptotically stable if R_(0)>1 and τl=0.Finally,we give numerical simulations toverify our results.

Adequacy of Logistic models for describing the dynamics of COVID-19 pandemic

Logistic models have been widely used for modelling the ongoing COVID-19 pandemic.This study used the data for Kuwait to assess the adequacy of the two most commonly used logistic models(Verhulst and Richards models)for describing the dynamics COVID-19.Specifically,the study assessed the predictive performance of these two models and the practical identifiability of their parameters.Two model calibration approaches were adopted.In the first approach,all the data was used to fit the models as per the heuristic model fitting method.In the second approach,only the first half of the data was used for calibrating the models,while the other half was left for validating the models.Analysis of the obtained calibration and validation results have indicated that parameters of the two models cannot be identified with high certainty from COVID-19 data.Further,the models shown to have structural problems as they could not predict reasonably the validation data.Therefore,they should not be used for long-term predictions of COVID-19.Suggestion have been made for improving the performances of the models.

Infection-acquired versus vaccine-acquired immunity in an SIRWS model

In some disease systems,the process of waning immunity can be subtle,involving a complex relationship between the duration of immunitydacquired either through natural infection or vaccinationdand subsequent boosting of immunity through asymptomatic reexposure.We present and analyse a model of infectious disease transmission where primary and secondary infections are distinguished to examine the interplay between infection and immunity.Additionally we allow the duration of infection-acquired immunity to differ from that of vaccine-acquired immunity to explore the impact on long-term disease patterns and prevalence of infection in the presence of immune boosting.Our model demonstrates that vaccination may induce cyclic behaviour,and the ability of vaccinations to reduce primary infections may not lead to decreased transmission.Where the boosting of vaccine-acquired immunity delays a primary infection,the driver of transmission largely remains primary infections.In contrast,if the immune boosting bypasses a primary infection,secondary infections become the main driver of transmission under a sufficiently long duration of immunity.Our results show that the epidemiological patterns of an infectious disease may change considerably when the duration of vaccine-acquired immunity differs from that of infection-acquired immunity.Our study highlights that for any particular disease and associated vaccine,a detailed understanding of the waning and boosting of immunity and how the duration of protection is influenced by infection prevalence are important as we seek to optimise vaccination strategies.

Dynamic model of tuberculosis considering multi-drug resistance and their applications

Infectious diseases have always been a problem that threatens people's health and tuberculosis is one of the major.With the development of medical scientific research,drug-resistant infectious diseases have become a more intractable threat because various drugs and antibiotics are widely used in the process of fighting against infectious diseases.In this paper,an improved dynamic model of infectious diseases considering population dynamics and drug resistance is established.The feasible region,equilibrium points and stability of the model are analyzed.Based on the existing data,this model can predict the development of the epidemic situation through numerical simulation,and put forward some relevant measures and suggestions.