Global stability for age-infection-structured human immunodeficiency virus model with heterogeneous transmission.

ABSTRACT

In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R0. If R0<1, disease-free equilibrium is globally asymptotically stable. If R0>1, it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for R0 is performed by the method of partial rank correlation coefficient(PRCC).