提出了一类具有潜伏感染细胞的时滞HIV-1传染病模型，定义了基本再生数R0，给出了无病平衡点P0（x0，0，0，0）和慢性感染平衡点P*（x*，ω*，y*，v*）的存在条件.首先利用线性化方法，得到了无病平衡点和慢性感染平衡点的局部渐近稳定性.进一步通过构造相应的Lyapunov函数，并结合LaSalle不变集原理，证明了当R0≤1时，无病平衡点P0（x0，0，0，0）是全局渐近稳定的；当R0>1时，慢性感染平衡点P*（x*，ω*，y*，v*）是全局渐近稳定的，但无病平衡点P0（x0，0，0，0）是不稳定的.结果表明，模型中的潜伏感染时滞和感染时滞并不影响模型的全局稳定性，并通过数值模拟验证了所得结论.
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.
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中国综合性科技类核心期刊(北大核心)