Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate

Yang Chen; Wencai Zhao; Yang Chen; Wencai Zhao

doi:10.3934/mbe.2020316

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5925-5943. doi: 10.3934/mbe.2020316

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Research article

Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate

Yang Chen ,
Wencai Zhao ^,

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 22 June 2020 Accepted: 24 August 2020 Published: 08 September 2020

In this paper, a stochastic SIRS epidemic model with saturating contact rate is constructed. First, for the deterministic system, the stability of the equilibria is discussed by using eigenvalue theory. Second, for the stochastic system, the threshold conditions of disease extinction and persistence are established. Our results indicate that a large environmental noise intensity can suppress the spread of disease. Conversely, if the intensity of environmental noise is small, the system has a stationary solution which indicates the disease is persistent. Eventually, we introduce some computer simulations to validate the theoretical results.
- stochastic SIRS epidemic model,
- saturating contact rate,
- extinction,
- persistence,
- stationary solution
Citation: Yang Chen, Wencai Zhao. Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5925-5943. doi: 10.3934/mbe.2020316

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Abstract

In this paper, a stochastic SIRS epidemic model with saturating contact rate is constructed. First, for the deterministic system, the stability of the equilibria is discussed by using eigenvalue theory. Second, for the stochastic system, the threshold conditions of disease extinction and persistence are established. Our results indicate that a large environmental noise intensity can suppress the spread of disease. Conversely, if the intensity of environmental noise is small, the system has a stationary solution which indicates the disease is persistent. Eventually, we introduce some computer simulations to validate the theoretical results.

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