Stationary distribution and density function of a stochastic SVIR epidemic model

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 station-ary 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. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, we investigate the long-term properties of a stochastic SVIR epidemic model with saturation incidence rates and logistic growth. We derive the fitness of a unique global positive solution, establish appropriate Lyapunov functions, and determine conditions for the existence of stationary distribution and persistence in the mean. We also identify conditions for exponential extinction of infected individuals. Furthermore, we use the Fokker-Planck equation and stochastic analysis to derive the probability density function around the quasi-endemic equilibrium point. The main theoretical results are verified through examples and illustrative simulations.