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. The model is described by equations containing ordinary differential equations and partial differential equations, taking into account factors such as vertical infection, age of onset, hope of AIDS patients to return to latent period, and the ability of different patients to receive treatment. The equation is directly introduced: when the mortality caused by AIDS increases, the total population declines, the fitness of the system is analyzed by using the functional analysis method and the bounded linear operator semigroup theory, and the existence of positive solutions of the system equations is proved.