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Luo, Q., Mao, X. and Shen, Y. (2011) Generalised Theory on Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations. Automatica, 47, 2075-2081.
https://doi.org/10.1016/j.automatica.2011.06.014

has been cited by the following article:

• 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.