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.
Highlights
A Stochastic SIVS Epidemic Model Based on Birth and Death ProcessCollege of Science, University of Shanghai for Science and Technology, Shanghai, China
A great interest in the analysis and prediction of consequences of public health strategies designed to control infectious disease, tuberculosis and (Acquired Immune Deficiency Syndrome) AIDS [1], has arised
The continuous time Markov chain model and the stochastic differential equation model based on birth and death process [4] [14] [16] are formulated based on the deterministic epidemic model
Summary
College of Science, University of Shanghai for Science and Technology, Shanghai, China. How to cite this paper: Zhu, L. and Zhang, T.S. (2016) A Stochastic SIVS Epidemic Model Based on Birth and Death Process. Journal of Applied Mathematics and Physics, 4, 18371848. Received: August 13, 2016 Accepted: September 26, 2016 Published: September 29, 2016
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