Author(s)

Modeste N’zi¹, Boubacar Sidiki Kouyaté^2*, Ilimidi Yattara², Modibo Diarra²

¹Laboratory of Applied Mathematics and Computer Science, University Felix Houphouet-Boigny, Abidjan, Côte d’Ivoire.
²Department of Mathematics and Computer Science, University of Science, Technic and Technologies, Bamako, Mali.

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.

SIRS Delayed Epidemic Model, Nonlinear Incidence rate, Lyapunov Function, Asymptotic Stability in Probability

N’zi, M. , Kouyaté, B. , Yattara, I. and Diarra, M. (2024) Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility. Journal of Applied Mathematics and Physics, 12, 509-532. doi: 10.4236/jamp.2024.122034.