Global stability of nonlinear stochastic SEI epidemic model with fluctuations in transmission rate of disease (Q507683)

Summary: 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 (\(R_0\)) and stochastic (\(\mathcal{R}_0\)) 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., \(R_0 < 1\)), epidemic can still grow initially (if \(\mathcal{R}_0 > 1\)) 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.