Two Kinds Of Bacteria Infection Dynamical Models With Age Structure

According to the characteristics of bacterial contamination of environment spread in the crowd, we establish and analyze two kinds of bacteria infection dynamics models with age structure in this paper. One is a bacterial infection dynamical model with immune of age structure, another is bacterial infection dynamical model with vaccination age structure. Using the theory and methods of dynamics differential equation, we analyze the global dynamics of the model,and obtain the existence of the basic reproductive number.The disease-free equilibrium and the epidemic equilibrium of system are obtained.Using the methods of characteristical equation,we analyze the stability of the equilibrium of the system and the local asymptotic stability of the disease-free equilibrium state E0,when R0≤1 ; When R0> 1, the disease-free equilibrium E0 is local instability, the local disease equilibrium E* is local stability; Useing the infinite dimensional dynamical system persistence theory, we analyze the persistence of the system. When R0 > 1, system disease persistence; Finally, we analyze the global stability of the equilibrium state of the model through the construction of a Lyapunov function. When the basic reproduction number R0 ≤ 1, the disease-free equilibrium E0 is globally asymptotically stable; When R0 > 1, the local disease equilibrium E* is globally asymptotically stable.