期刊
AIMS MATHEMATICS
卷 8, 期 10, 页码 25037-25059出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20231278
关键词
stochastic SIR model; extinction; persistence in the mean; stochastic Lyapunov function; stationary distribution
This paper studies a stochastic SIR model with nonlinear incidence and recovery rate. It proves the existence of a unique global positive solution for any initial value of the system, provides sufficient conditions for disease extinction or persistence, and analyzes the influence of the threshold & SIM;R0 of the stochastic SIR model on disease state transition. Additionally, it proves that the system has a stationary distribution under some given parameter conditions by building an appropriate stochastic Lyapunov function and using the equivalent condition of the Hasminskii theorem. Finally, the correctness of these theoretical results are validated by numerical simulations.
The spread of infectious diseases are inevitably affected by natural and social factors, and their evolution presents oscillations and other uncertainties. Therefore, it is of practical significance to consider stochastic noise interference in the studies of infectious disease models. In this paper, a stochastic SIR model with nonlinear incidence and recovery rate is studied. First, a unique global positive solution for any initial value of the system is proved. Second, we provide the sufficient conditions for disease extinction or persistence, and the influence of threshold & SIM;R0 of the stochastic SIR model on disease state transition is analyzed. Additionally, we prove that the system has a stationary distribution under some given parameter conditions by building an appropriate stochastic Lyapunov function as well as using the equivalent condition of the Hasminskii theorem. Finally, the correctness of these theoretical results are validated by numerical simulations.
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