Asympotic Analysis of SEIS Model with General Saturated Contact Rate

In this paper,a kind of SEIS model with general saturated contact rate is studied and the threshold,a basic reproductive number which determines the outcome of the infectious disease is found.When R_01 there only exists a globally asymptotically stable disease free equi- librium p~0;whenR_01,two equilibria,a locally asymptotically stable equilibrium P~* and an unstable disease free equilibrium p~0 exist;when R_0=1,there only exists disease free equilibrium p~0.Specially,if the death rate due to disease equals zero,the endemic equilibrium of the limit equation is globally asymptotically stable.