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

Authors

Olusegun Michael Otunuga, Marshall UniversityFollow

Document Type

Article

Publication Date

1-23-2017

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 (R₀) and stochastic (R₀) 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., R₀ < 1), epidemic can still grow initially (if R₀ > 1) 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.

Comments

The copy of record is available from the publisher at https://doi.org/10.1155/2017/6313620.

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.

Recommended Citation

O. M. Otunuga, “Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission rate of Disease,” International Journal of Stochastic Analysis, vol. 2017, Article ID 6313620, pp 1-7, 2017.