Asymptotic analysis of a stochastic SVEIS epidemic model using Black-Karasinski process

TL;DR

This paper analyzes a stochastic epidemic model incorporating a Black-Karasinski process, providing conditions for disease persistence or extinction, and demonstrating how randomness influences outbreak dynamics.

Contribution

It introduces a stochastic SVEIS epidemic model with Black-Karasinski perturbation and derives conditions for disease persistence and extinction using Lyapunov methods.

Findings

Disease persists if Rs0>1

Disease dies out exponentially if Re0<1

Random fluctuations facilitate outbreaks

Abstract

In this paper, we present a stochastic SVEIS epidemic model perturbed by a Black-Karasinski process. Using a Lyapunov functional approach, we derive a sufficient condition, Rs0>1 for the existence of a stationary distribution, which indicates disease persistence. Additionally, we theoretically demonstrate that the disease will die out at an exponential rate if Re0<1 . Our results show that random fluctuations will facilitate disease outbreak.