Dynamic behavior of a stochastic SIR model with nonlinear incidence and recovery rates

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.

Automated summary

This paper studies a stochastic SIR model with nonlinear incidence and recovery rate. The paper proves the existence of a unique global positive solution for any initial value of the system. It also provides sufficient conditions for disease extinction or persistence and analyzes the influence of threshold and R0 on disease state transition in the stochastic SIR model. Additionally, the paper demonstrates the system's stationary distribution under certain parameter conditions and validates the theoretical results through numerical simulations.