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: Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets

  AUTHORS: Boubacar Sidiki Kouyaté, Modeste N’zi

  KEYWORDS: Vector-Borne Disease Epidemic Model, Stochastic Delay Differential Equations, Stochastic Stability, Lyapunov Functional Technique

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.1, January 31, 2024

  ABSTRACT: Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.