Abstract

In this talk, we first consider a SIVR  model which combines impulsive vaccination into the classical SIR model. The final size, the peak value and peak time are studied, then the critical times for a given infected number is discussed, and it can be used to define and estimate the stopping time. Finally, a diffusion SIS model is proposed to study the spatial spreading of virus. The free boundary is introduced to describe the spreading front of the infected interval. To check the effect of spatial heterogeneity and habitat characteristic on the spreading of the virus, the spatial-temporal risk index is given. Our results show that the virus will spread in the high-risk habitat; in a low-risk habitat, small initial infected habitat, small initial numbers of the virus and fast diffusion are beneficial for the virus to vanish. When the virus spreads in the whole habitat, the asymptotic spreading speed is given.