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Global Dynamics of a Multi-group SEIR Epidemic Model with infection age

Chinese Annals of Mathematics,Series B 2021年第6期42卷 833-860页

作者： Vijay Pal BAJIYA Jai Prakash TRIPATHI Vipul KAKKAR Jinshan WANG Guiquan SUN Department of Mathematics Central University of RajasthanBandar Sindri-305817KishangarhAjmerRajasthanIndia Complex Systems Research Center Shanxi UniversityTaiyuan 030006China Department of Mathematics North University of ChinaTaiyuan 030051China Complex Systems Research Center Shanxi UniversityTaiyuan 030006China.

Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.

关键词： Multi-group model infection age Feedback Graph-theoretic approach Lyapunov function

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SIVS EPIDEMIC MODELS WITH infection age AND NONLINEAR VACCINATION RATE

引用

Annals of Differential Equations 2010年第4期26卷 471-476页

作者： Junyuan Yang 1,2 , Xiaoyan Wang 1 , Fengqin Zhang 1 (1. Dept. of Math., Yuncheng University, Yuncheng 044000, ShanXi 2. Beijing Institute of Information and Control, Beijing 100037)

Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.

关键词： epidemic model infection age vaccination reproductive number

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