Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence

Huyi Wang, Ge Zhang, Tao Chen and Zhiming Li ()
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Huyi Wang: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Ge Zhang: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Tao Chen: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Zhiming Li: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Mathematics, 2023, vol. 11, issue 7, 1-17

Abstract: The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value ( R 0 m ) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R 0 m < 1 , the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R 0 m > 1 , the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease.

Keywords: stochastic SIRS epidemic model; Logistic birth; nonlinear incidence; global stability; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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