| In reality, there are various diseases. In this paper, firstly, the local stabil-ity of the SIR models with age-structured and vertical transmission in different vaccination is studied, one is for all people, the other is for fixed age. Secondly, the delayed SDIR model is established to study the problem of two kinds disease which can’t overlap existing at same time. The incidence of the first disease is β1S(t)I1(t),the second isβ2S(t)I2(t)/1+α2I2(t) Through the qualitative analysis of this mod-el, the related thresholds R1,R2,R3are got. Furthermore, when R1,R2,R2are under particular constraints, the model has a disease-free equilibriums and three endemic equilibriums. Based on the traditional methods of constructing Lya-punov function used in SIR model, a particular Lyapunov function is set up for the SDIR model I established. According to invariant set principle, the asymp-totic stability of a disease-free equilibriums and three endemic equilibriums are studied when R1,R2,R3satisfy a certain constraints. At last, by comprehensive analysis of these results, the coupled effect of these two kinds of diseases during spreading is obtained and a robust safety precaution is proposed when these two diseases outbreak in reality. It has some certain practical significance for precau-tion and controlling of infectious disease. |
