Author(s)

Lin Zhu, Tiansi Zhang^*

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

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.

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

Zhu, L. and Zhang, T. (2016) A Stochastic SIVS Epidemic Model Based on Birth and Death Process. Journal of Applied Mathematics and Physics, 4, 1837-1848. doi: 10.4236/jamp.2016.49186.