GLOBAL STABILITY AND SPATIAL SPREAD OF THE NONLINEAR EPIDEMIC MODEL

Abstract

In this paper, we consider a non linear epidemic model SIQS by experiencing the disease; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local stabilities and global stability of the infection-free equilibrium and endemic equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and after we stydy local and global asymptotic stability. We study the stochastique systme by pertubing the contact rate, and we mainly use the theorie of Itô formula. Finnaly we study the spatial spread model with traveling wave solution.