Dynamical analysis of an age-structured multi-group SIVS epidemic model

Junyuan Yang; Rui Xu; Xiaofeng Luo; Junyuan Yang; Rui Xu; Xiaofeng Luo

doi:10.3934/mbe.2019031

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 636-666. doi: 10.3934/mbe.2019031

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Research article

Dynamical analysis of an age-structured multi-group SIVS epidemic model

1.
Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P.R. China
2.
Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, Shanxi 030006, P.R. China

Received: 22 December 2017 Accepted: 14 October 2018 Published: 14 January 2019

Host heterogeneities such as space, gender, and age etc are intrinsic characters for investigating diseases mechanisms and transmission routes. First, we incorporate inter-group, intra-group and age structure to propose a multi-group SIVS epidemic model. Then we obtain the basic reproduction number of the system which is the spectral radius of the next generation operator by the renewal equation. Based on some assumptions for parameters, we obtain the existence and uniqueness of endemic equilibrium. By means of integral semigroup theory and Lyapunov methods, we show that the threshold dynamics of the system is completely determined by the basic
- multi-group epidemic model,
- the next generation operator,
- global attractivity
Citation: Junyuan Yang, Rui Xu, Xiaofeng Luo. Dynamical analysis of an age-structured multi-group SIVS epidemic model[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 636-666. doi: 10.3934/mbe.2019031

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Abstract

Host heterogeneities such as space, gender, and age etc are intrinsic characters for investigating diseases mechanisms and transmission routes. First, we incorporate inter-group, intra-group and age structure to propose a multi-group SIVS epidemic model. Then we obtain the basic reproduction number of the system which is the spectral radius of the next generation operator by the renewal equation. Based on some assumptions for parameters, we obtain the existence and uniqueness of endemic equilibrium. By means of integral semigroup theory and Lyapunov methods, we show that the threshold dynamics of the system is completely determined by the basic

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