一类传染病模型阶段性感染的全局稳定性

Global Dynamics of a Staged Progression Model for Infectious Diseases

摘要: 本文讨论了一类传染病数学模型，分析了受感染宿主在不同阶段感染的情形，如由HIV病毒引起的艾滋病。对于其有双线性发生率的n阶段模型(SP)，本文证明了此类传染病模型的全局稳定性完全由基本再生数R₀决定，若R₀ ≤ 1，则无病平衡点P₀是全局渐进稳定，并且疾病会消失；若R₀ > 1，P₀是不稳定的，且唯一的地方性平衡点P*是渐进稳定的。

Abstract: We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AID, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R₀: If R₀ ≤ 1, then the dis-ease-free equilibrium P₀ is globally asymptotically stable and the disease always dies out. If R₀ > 1; P₀ is unstable, and a unique endemic equilibrium P* is globally asymptotically stable, and the dis-ease persists at the endemic equilibrium. The basic reproduction number for the SP model with density dependent incidence forms are also discussed.