具有染病者筛查和性别结构的随机AIDS传染病模型分析  

Analysis of a Stochastic Sex-Structured AIDS Epidemic Model with Effect of Screening of Infectives

作　　者：赵晓琦 董玲珍 

机构地区：[1]太原理工大学数学学院,山西 太原

出　　处：《应用数学进展》2021年第4期1153-1167,共15页Advances in Applied Mathematics

摘　　要：本文主要研究了具有染病者筛查和性别结构的随机AIDS传染病模型,利用ITO公式,讨论了该系统的动力学行为。首先,我们证明了该模型解的极限性质;其次,通过选取合适的对数函数,给出了疾病灭绝的充分条件;进一步,选取恰当的V函数,分析了系统唯一正的遍历平稳分布的存在性;最后,通过数值模拟,验证了本文的理论结果。In this paper, we study a stochastic model describing the sex-structured AIDS with effect of screening of infectives, and the dynamic behavior of the system is discussed by using the formula of ITO. First, we consider the limiting behaviors of the solution. Further, the sufficient condition guaranteeing the extinction of AIDS is obtained. Then, an appropriate V-function is selected to prove that the solution of the model has a unique ergodic stationary distribution. Finally, the theoretical results are verified by numerical simulations.

关 键 词：性别结构AIDS模型 随机系统 ITO公式 灭绝 遍历平稳分布 

分 类 号：R51[医药卫生—内科学]