关键词: HIV-1传染病模型, 潜伏感染细胞, 时滞, Lyapunov函数

Abstract: A class of delayed HIV-1 infection models with latently infected cells was proposed. The basic reproductive number R₀ was defined, and the existence conditions of disease-free equilibrium P₀(x₀, 0, 0, 0) and chronic-infection equilibrium P^*(x^*, ω^*, y^*, v^*) were given. First, the local asymptotic stability of infection-free equilibrium and chronicinfection equilibrium was obtained by the linearization method. Further, by constructing the corresponding Lyapunov functions and using LaSalle's invariant principle, it was proved that when the basic reproductive number R₀ was less than or equal to unity, the infection-free equilibrium P₀(x₀, 0, 0, 0) was globally asymptotically stable; moreover, when the basic reproductive number R₀ was greater than unity, the chronic-infective equilibrium P^*(x^*, ω^*, y^*, v^*) was globally asymptotically stable, but the infection-free equilibrium P₀(x₀, 0, 0, 0) was unstable. The results showed that a latently infected delay and an intracellular delay did not affect the global stability of the model, and numerical simulations were carried out to illustrate the theoretical results.

Key words: HIV-1 infection model, latently infected cells, delay, Lyapunov function