Asymptotical stability analysis of a SEIS epidemic model with infectious force in both latent period and infected period

A SEIS epidemic model with infective force in both latent period and infected period,having different general saturated contact rate C1(N) and C2(N),is studied and the basic reproductive number R0 is obtained.By using Liapunov function method,it is proved that the disease-free equilibrium P0 is globally asymptotically stable and the disease always dies out eventually if R01.It is also proved that in the case where R01,P0 is unstable and the unique endemic equilibrium P* is locally asymptotically stable by Hurwitz criterion theory.It is shown that when disease-induced death rate is zero,the unique endemic equilibrium P～* of the limiting system is globally asymptotically stable.