Dynamical behavior of a multigroup SIRS epidemic model with standard incidence rates and Markovian switching

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.3934/dcds.2019249

Article Contents

2019, Volume 39, Issue 10: 5683-5706. Doi: 10.3934/dcds.2019249

This issue Previous Article Slices of parameter spaces of generalized Nevanlinna functions Next Article An operator splitting scheme for the fractional kinetic Fokker-Planck equation

Dynamical behavior of a multigroup SIRS epidemic model with standard incidence rates and Markovian switching

a.
School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal Universit, Changchun 130024, Jilin Province, China
b.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia
c.
College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, China
d.
Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan

^* Corresponding author at School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin 130024, China
^* Corresponding author at School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin 130024, China

Received: May 31, 2018

Published: July 2019

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Abstract

In this paper, we consider a multigroup SIRS epidemic model with standard incidence rates and Markovian switching. Firstly, we obtain sufficient conditions for extinction of the diseases. Then we establish sufficient conditions for persistence in the mean of the diseases. Moreover, in the case of persistence, we derive sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.

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Mathematics Subject Classification: Primary: 34E10, 60H10; Secondary: 92B05, 92D30.

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