RESEARCH
Persistence and extinction of an SIS epidemic model with regime switching and L\'evy jumps

2020-10-23　14:00 — 15:00

This talk is devoted to a stochastic regime-switching susceptible-infected-susceptible epidemic model with nonlinear incidence rate and L\'evy jumps. A threshold $\lambda$ in terms of the invariant measure, different from the usual basic reproduction number, is obtained to completely determine the extinction and prevalence of the disease: if $\lambda>0$, the disease is persistent and there is a stationary distribution; if $\lambda<0$, the disease goes to extinction and the susceptible population converges weakly to a boundary distribution. Moreover, some numerical simulations are performed to illustrate our theoretical results. It is very interesting to notice that random fluctuations (including the white noise and L\'evy noise) acting the infected individuals can prevent the outbreak of disease, that the disease of a regime-switching model may have the opportunity to persist eventually even if it is extinct in one regime, and that the prevalence of the disease can also be controlled by reducing the value of transmission rate of disease.