### Mathematical Biosciences and Engineering

2020, Issue 5: 5925-5943. doi: 10.3934/mbe.2020316
Research article

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

• 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.

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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• 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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