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Capasso, V. and Bakstein, D. (2005) An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine. Birkhäuser, New York.

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.