Kirschner D, Webb G F
Department of Mathematics, Texas A&M University, College Station 77845, USA. dek/math.tamu.edu
Bull Math Biol. 1996 Mar;58(2):376-90. doi: 10.1016/0092-8240(95)00345-2.
Mathematical models are developed for the chemotherapy of AIDS. The models are systems of differential equations describing the interaction of the HIV infected immune system with AZT chemotherapy. The models produce the three types of qualitative clinical behavior: an uninfected steady state, an infected steady state (latency) and a progression to AIDS state. The effect of treatment is to perturb the system from progression to AIDS back to latency. Simulation of treatment schedules is provided for the consideration of treatment regimes. The following issues of chemotherapy are addressed: (i) daily frequency of treatment, (ii) early versus late initiation of treatment and (iii) intermittent treatment with intervals of no treatment. The simulations suggest the following properties of AZT chemotherapy: (i) the daily period of treatment does not affect the outcome of the treatment, (ii) treatment should not begin until after the final decline of T cells begins (not until the T cell population falls below approximately 300 mm-3) and then, it should be administered immediately and (iii) a possible strategy for treatment which may cope with side effects and/or resistance, is to treat intermittently with chemotherapy followed by interruptions in the treatment during which either a different drug or no treatment is administered. These properties are revealed in the simulations, as the model equations incorporate AZT chemotherapy as a weakly effective treatment process. We incorporate into the model the fact that AZT treatment does not eliminate HIV, but only restrains its progress. The mathematical model, although greatly simplified as a description of an extremely complex process, offers a means to pose hypotheses concerning treatment protocols, simulate alternative strategies and guide the qualitative understanding of AIDS chemotherapy.
针对艾滋病化疗建立了数学模型。这些模型是描述感染HIV的免疫系统与齐多夫定（AZT）化疗相互作用的微分方程组。这些模型产生三种定性的临床行为：未感染稳态、感染稳态（潜伏期）和进展至艾滋病状态。治疗的效果是使系统从进展至艾滋病状态扰动回到潜伏期。提供了治疗方案的模拟，以供考虑治疗方案。探讨了化疗的以下问题：（i）每日治疗频率，（ii）治疗的早期启动与晚期启动，以及（iii）有不治疗间隔的间歇治疗。模拟结果表明了AZT化疗的以下特性：（i）每日治疗周期不影响治疗结果，（ii）治疗应在T细胞最终下降开始后（直到T细胞数量降至约300mm-3以下）才开始，然后应立即给药，以及（iii）一种可能应对副作用和/或耐药性的治疗策略是间歇化疗，随后在治疗期间中断，在此期间要么给予不同药物要么不治疗。这些特性在模拟中得以揭示，因为模型方程将AZT化疗作为一个弱有效治疗过程纳入其中。我们将AZT治疗不能消除HIV但只能抑制其进展这一事实纳入模型。该数学模型虽然作为对极其复杂过程的描述被极大简化，但提供了一种提出关于治疗方案的假设、模拟替代策略并指导对艾滋病化疗进行定性理解的方法。
