Analysis Of An Age-structured Epidemic Model With Latent Period

The health of human are threatened by infectious diseases which also bring a greatlosses to social economy. Therefore, there is of great importance to study epidemic mod-els. An age-structured epidemic model with latent period is considered in this paper whichconsists of the following two parts:In the second chapter, a SEIS epidemic model with age of infection is considered. Thebasic reproductive number R₀is established for the model by using the theory of difer-ential and integral equations. It is proved that the disease free equilibruim is globallyasymptotically stable if R₀<1. The disease free equilibruim is unstable if R₀>1whenthe endemic equilibruim is locally asymptotically stable.In the third chapter, an age-structured MSEIS model is considered, in which a certainpercentage of susceptibles could enter the infectious class without experiencing the latentperiod. By using the theory of diferential and integral equations, the explicit expressionof the basic reproductive number R₀was obtained. It is proved that the disease freeequilibruim is globally asymptotically stable if R₀<1. The disease free equilibruim isunstable if R₀>1, and there at least exist one endemic equilibruim which can be provedthat it is locally asymptotically stable under centain conditions.