Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1.
J Biol Dyn. 2008 Apr;2(2):154-68. doi: 10.1080/17513750802120877.
We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as highly active antiretroviral therapy. For a general n-stage model with constant recruitment and bilinear incidence that incorporates amelioration, we prove that the global dynamics are completely determined by the basic reproduction number R(0). If R(0)≤1, then the disease-free equilibrium P(0) is globally asymptotically stable, and the disease always dies out. If R(0)>1, P(0) is unstable, a unique endemic equilibrium P* is globally asymptotically stable, and the disease persists at the endemic equilibrium. Impacts of amelioration on the basic reproduction number are also investigated.
我们分析了一个传染病数学模型的全局动态，该模型在受感染宿主中经历不同阶段，且具有改善的可能性。HIV/AIDS 就是这样一种疾病，它经历了几个不同程度传染性的阶段；改善可能来自宿主的免疫反应，更常见的是来自抗逆转录病毒疗法，如高效抗逆转录病毒疗法。对于一个具有常数招募和双线性发生率且包含改善的一般 n 阶段模型，我们证明了全局动态完全由基本繁殖数 R(0)决定。如果 R(0)≤1，则无病平衡点 P(0)全局渐近稳定，疾病总是消失。如果 R(0)>1，则 P(0)不稳定，存在唯一的地方平衡点 P*，疾病在地方平衡点持续存在。还研究了改善对基本繁殖数的影响。
