The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence

Abstract

We investigate degenerate stochastic SIR epidemic model with saturated incidence. For the constant coefficients case, we achieve a threshold which determines the extinction and persistence of the epidemic by utilizing Markov semigroup theory. Furthermore, we conclude that environmental white noise plays a positive effect in the control of infectious disease in some sense comparing to the corresponding deterministic system. For the stochastic non-autonomous system, we prove the existence of periodic solution.

Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine

“…The birth rate, death rate, recovery rate and other parameters appear more or less periodicity rather than keeping constant, and hence it is reasonable to further take periodic variation into account in the process of investigating the stochastic epidemic model. The existence of periodic solutions is important for understanding and controlling the transmissibility of the diseases, and is extensively researched as a key point in many literatures [38][39][40][41][42][43][44]. For instance, Lin et al [39] researched a stochastic non-autonomous periodic SIR model and established the threshold of the disease to occur and also verified the existence of periodic solutions.…”