An SS<sub>m</sub>EIA AIDS Model Influenced by Information and Classified Consciously

针对艾滋病的特点，考虑现实生活中信息对于疾病传播的影响，建立了一类受信息影响且具有意识分类的SSmEIA模型。首先利用再生矩阵的方法给出了模型的基本再生数，接着给出模型的无病平衡点和地方病平衡点并利用Routh-Hurwitz判据和LaSalle不变集原理证明出了两类平衡点的稳定性。其次，选取河南省艾滋病累计病例数据，利用最小二乘法进行数值估计并给出拟合图。最后对模型部分参数进行敏感性分析，分析得出提高大众对于艾滋病信息的认识、扩大艾滋病宣传范围能够有效减少艾滋病的感染率，进一步遏制艾滋病扩散。In view of the characteristics of AIDS and considering the impact of information on disease transmission in real life, an SSmEIA model with awareness classification affected by information is established. Firstly, the basic reproduction number of the model is given using the method of regeneration matrix. Then, the disease-free equilibrium point and endemic equilibrium point of the model are given, and the stability of the two types of equilibrium points is proved using Routh Hurwitz criterion and LaSalle invariant set principle. Secondly, the cumulative case data of AIDS in Henan Province is selected, and the least square method is used to estimate the numerical value and give the fitting diagram. Finally, the sensitivity analysis of some parameters of the model shows that improving public awareness of AIDS information and expanding the scope of AIDS publicity can effectively reduce the infection rate of AIDS and further curb the spread of AIDS.