TY - JOUR
T1 - Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease
AU - Otunuga, Olusegun Michael
N1 - Publisher Copyright:
© 2017 Olusegun Michael Otunuga.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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U2 - 10.1155/2017/6313620
DO - 10.1155/2017/6313620
M3 - Article
AN - SCOPUS:85012118480
SN - 2090-3332
VL - 2017
JO - International Journal of Stochastic Analysis
JF - International Journal of Stochastic Analysis
M1 - 6313620
ER -