SIR epidemic model with non-Lipschitz stochastic perturbations

Shuang Li and Jie Xiong

Statistics & Probability Letters, 2024, vol. 210, issue C

Abstract: This paper investigates a stochastic SIR epidemic model with non-Lipschitz coefficients in the diffusion term. Firstly, we study the existence and uniqueness of the global positive solution of this model. Then, we prove that the stochastic process has a stationary distribution, and we also establish an exact expression of the density function of the stationary distribution under certain parameter constraints. Finally, we discuss the extinction of the epidemic and the asymptotic properties around the equilibrium points of the deterministic SIR model.

Keywords: Stochastic SIR epidemic model; Non-Lipschitz coefficient; Stationary distribution; Extinction; Asymptotic behavior (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110109

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