具有心理效应和媒体影响的随机HIV/AIDS传染病模型

Random HIV/AIDS infectious disease model with psychological and media effects

建立了一类满足Logistic人口增长方程且同时具有心理效应和媒体影响的随机HIV/AIDS传染病模型,通过构造相应的Lyapunov函数,利用停时理论、伊藤引理及强大数定理等对随机HIV/AIDS传染病模型进行了理论分析,进而证明了随机模型全局正解的存在唯一性,并且通过对相应Lyapunov函数的计算研究,给出了疾病灭绝和持久的充分条件.最后,利用最小二乘法和Euler-Maruyama方法对随机传染病模型进行数值模拟,进一步显示了随机传染病模型的动力学行为.

A random HIV/AIDS epidemic model satisfying the Logistic population growth equation with both psychological effects and media influences was established.By constructing the corresponding Lyapunov function,the existence and exclusivity of the global positive solution of the model are proved by theoretical analysis using It's lemma lemma and strong number theorem,and sufficient conditions for the extinction and persistence of the disease are given.Finally,the least square method and Euler-Maruyama method are used to verify the theoretical results.