Almost periodic solutions for a SVIR epidemic model with relapse

Yifan Xing; Hong-Xu Li; Yifan Xing; Hong-Xu Li

doi:10.3934/mbe.2021356

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 7191-7217. doi: 10.3934/mbe.2021356

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Almost periodic solutions for a SVIR epidemic model with relapse

Yifan Xing ,
Hong-Xu Li ^,

College of Mathematics, Sichuan University, Chengdu 610065, China

Academic Editor: Haiyan Wang

Received: 14 June 2021 Accepted: 11 August 2021 Published: 26 August 2021

This paper is devoted to a nonautonomous SVIR epidemic model with relapse, that is, the recurrence rate is considered in the model. The permanent of the system is proved, and the result on the existence and uniqueness of globally attractive almost periodic solution of this system is obtained by constructing a suitable Lyapunov function. Some analysis for the necessity of considering the recurrence rate in the model is also presented. Moreover, some examples and numerical simulations are given to show the feasibility of our main results. Through numerical simulation, we have obtained the influence of vaccination rate and recurrence rate on the spread of the disease. The conclusion is that in order to control the epidemic of infectious diseases, we should increase the vaccination rate while reducing the recurrence rate of the disease.
- epidemic model,
- persistence,
- almost periodic solution
Citation: Yifan Xing, Hong-Xu Li. Almost periodic solutions for a SVIR epidemic model with relapse[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7191-7217. doi: 10.3934/mbe.2021356

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Abstract

This paper is devoted to a nonautonomous SVIR epidemic model with relapse, that is, the recurrence rate is considered in the model. The permanent of the system is proved, and the result on the existence and uniqueness of globally attractive almost periodic solution of this system is obtained by constructing a suitable Lyapunov function. Some analysis for the necessity of considering the recurrence rate in the model is also presented. Moreover, some examples and numerical simulations are given to show the feasibility of our main results. Through numerical simulation, we have obtained the influence of vaccination rate and recurrence rate on the spread of the disease. The conclusion is that in order to control the epidemic of infectious diseases, we should increase the vaccination rate while reducing the recurrence rate of the disease.

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