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)

[thumbnail of Li-etal-JFI-2022-Stationary-distribution-and-density-function-of-a-stochastic-SVIR-epidemic-model]
Preview
 Text. Filename: Li_etal_JFI_2022_Stationary_distribution_and_density_function_of_a_stochastic_SVIR_epidemic_model.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (1MB)| Preview

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.

ORCID iDs

Li, Dan, Wei, Fengying and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)