Stationary distribution and density function of a stochastic SVIR epidemic model

Li, Dan and Wei, Fengying and Mao, Xuerong (2022) Stationary distribution and density function of a stochastic SVIR epidemic model. Journal of the Franklin Institute. ISSN 0016-0032 (https://doi.org/10.1016/j.jfranklin.2022.09.026)

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Abstract

We consider the long-term properties of a stochastic SVIR epidemic model with saturation incidence rates and logistic growth in this paper. We firstly derive the fitness of a unique global positive solution. Then we construct appropriate Lyapunov functions and obtain condition Rs 0 > 1 for existence of stationary distribution, and conditions for persistence in the mean. Moreover, conditions including Re 0 < 1 for exponential extinction to the infected individuals are figured out. Finally, by employing Fokker-Planck equation and stochastic analysis, we derive the probability density function around the quasi-endemic equilibrium point when critical value R p 0 > 1 is valid. Consequently, some examples and illustrative simulations are carried out to verify the main theoretical results.

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