TITLE:
Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility
AUTHORS:
Modeste N’zi, Boubacar Sidiki Kouyaté, Ilimidi Yattara, Modibo Diarra
KEYWORDS:
SIRS Delayed Epidemic Model, Nonlinear Incidence rate, Lyapunov Function, Asymptotic Stability in Probability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.2,
February
29,
2024
ABSTRACT: In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.