The Stability Of The Zero Equilibrium Solution To Non-linear PDE Models With Age Structure

The main contents of this paper consist of two parts.The first part is to discuss the asymptotic behavior of a class of non-linear and non-autonomous population model with age structure. The mortality rate in this model depends on the total population size. The existence and uniqueness of solutions are proved and the sufficient conditions for the stability and global asymptotic stability of zero equilibrium solution are obtained.In the second part, a general SIS model with chronological age and infection age structure is formulated. We analyze the global dynamics of the model with a constructive iteration procedure. The base productive number R₀ is calculated using the next generation operator approach. We show that R₀ plays a sharp threshold role in determining the global dynamics, i.e., the zero equilibrium solution is globally asymptotically stable if R₀<1, while the zero equilibrium solution is not stable and exist a unique positive equilibrium solution if R₀>1 .