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Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate
1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
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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