带有发病年龄的HIV/AIDS传播的数学建模及分析

所建的模型是用含有常微分方程和偏微分方程的方程组来描述的,考虑了垂直感染,发病年龄,AIDS病人有希望恢复到潜伏期以及不同患者接受治疗的能力不同等诸多因素.利用导出的方程,直接推出:当AIDS引起死亡率增加时,社会总人口衰减.利用泛函分析方法和有界线性算子半群理论分析了系统的适定性,并证明了系统方程存在正解.

Modeling with the AIDS-age on HIV/AIDS Transmission and Its Analysis

In this paper,I formulate a dynamic HIV/AIDS model with vertical transmission, AIDS-age,and the different capacity of treatment.I assume that there is an imperfect vaccine with therapeutic effect,which induces reversal from the AIDS stage to asymptomatic stage. From this HIV/AIDS model described by coupled equations of partial differential equations and ordinary differential equations,I can get that the total population decreases when the death rate caused by AIDS is not equal to zero.By using method of functional analysis, especially the semigroup theory of linear operators on Banach space,I prove well-posed-ness of the model and existence of the positive solution.