Two Kinds Of The Vector-host Epidemic Dynamical Models With Age-since-infection And Multistrains

In this paper, we introduce and analyze two kinds of the age-since-infection vector-host dynam-ical models for the multi-strain infectious diseases. In the first model, we investigate and analyze the vector-host dynamical model with the age-since-infection infective host and multi-strain infec-tion.In the second model, the hosts population is structured with respect to the physical age of the hosts.and the susceptibility of the hosts is assumed to be age-dependent. The dynamical behaviors of the presented models is mathematically analyzed. In the following form, the two kinds of the pre-sented models are analyzed. According to the characteristics of the infected strains, the expressions of the invasion reproduction number and the possibility existence of the equilibria in the models are obtained. By constructing a class of Lyapunov functions, it is shown that if the invasion reproduction number of the model R0(1)≤1,R0(2)≤1, the unique disease-free equilibrium E0is globally asymptot-ically stable;and if the invasion reproduction number of the model R0(1)>1,R0(2)≤1the disease-free equilibrium E0is unstable. Finally, by using some infinity dimension dynamical behaviors of the different equations, the persistence of the disease is proved. By constructing a series of appropriate Lyapunov functions, it is showed that it is valid for the competitive exclusion principle of the strains in the multi-strain and age-since-infection vector-host epidemic models.