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International Journal of Stochastic Analysis
Volume 2017, Article ID 6313620, 7 pages
https://doi.org/10.1155/2017/6313620
Research Article

Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease

Department of Mathematics, Marshall University, One John Marshall Drive, Huntington, WV, USA

Correspondence should be addressed to Olusegun Michael Otunuga; ude.llahsram@agunuto

Received 23 October 2016; Accepted 4 January 2017; Published 23 January 2017

Academic Editor: Manuel Osvaldo Cáceres

Copyright © 2017 Olusegun Michael Otunuga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic () and stochastic () basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., ), epidemic can still grow initially (if ) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.