Discussion On An Age-infection-structured HIV Model With Vertical Transmission

Vertical transmission is one of the main characteristics of HIV/AIDS,and it's progress depends on infection age(duration since infection).According to the characteristics of HIV/AIDS,we study an infection age HIV model with vertical transmission.The population is divided into susceptible and infective,the susceptible population satisfies ordinary differential equation,and the infective popula-tion satisfies partial differential equations for the infection age.The uniqueness of the integral solution is proved by the bounded linear operator semigroup theory;By constructing the Lyapunov function,we investigate the asymptotic behavior of the steady states.If the basic reproduction R0<1,the stable infection-free state is globally asymptotically stable.If vertical transmission parameter and horizontal transmission parameters satisfy some conditions,and R0>1,then the endemic state is asymptotically stable.