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Henson, S.M., King, A.A., Costantino, R.F., Cushing, J.M., Dennis, B. and Desharnais, R.A. (2003) Explaining and Predicting Patterns in Stochastic Population Systems. Proceedings of the Royal Society of London B, 270, 1549-1553.

has been cited by the following article:

• TITLE: A Stochastic SIVS Epidemic Model Based on Birth and Death Process

  AUTHORS: Lin Zhu, Tiansi Zhang

  KEYWORDS: Epidemic Model, Vaccination, Continuous Time Markov Chain, Birth and Death Process, Stochastic Differential Equations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.9, September 29, 2016

  ABSTRACT: A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.