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

Juping Zhang; Linlin Wang; Zhen Jin

doi:10.1016/j.idm.2024.01.008

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

Infect Dis Model. 2024 Feb 7;9(2):437-457. doi: 10.1016/j.idm.2024.01.008. eCollection 2024 Jun.

Authors

Juping Zhang^{1

2}, Linlin Wang^{1

2}, Zhen Jin^{1

2}

Affiliations

¹ Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, 030006, China.
² Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, Shanxi, 030006, China.

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 $R_{0}$ . If $R_{0} < 1$ , disease-free equilibrium is globally asymptotically stable. If $R_{0} > 1$ , 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 $R_{0}$ is performed by the method of partial rank correlation coefficient(PRCC).

Keywords: Age-infection-structured; Basic reproductive number; Global stability; Lyapunov function; Sensitivity analysis.