一类具有VCT意识的随机HIV/AIDS模型的动力学分析  

Dynamic Analysis of a Random HIV/AIDS Model with VCT Awareness

作　　者：刘宗萱 张太雷[1] 蒋为平 LIU Zong-xuan;ZHANG Tai-lei;JIANG Wei-ping(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《数学的实践与认识》2024年第3期135-150,共16页Mathematics in Practice and Theory

基　　金：陕西省自然科学基础研究计划(2022JM-023)。

摘　　要：建立了一类具有自愿咨询和检测(VCT)意识的随机HIV/AIDS传染病模型,利用停时理论等方法证明了随机模型正解的全局存在唯一性.其次,分析了该随机模型的解在相应确定性模型的无病平衡点与地方病平衡点附近的渐近行为,并得到了随机模型解的平均持续与灭绝性的充分条件.最后,通过数值模拟进一步显示了模型的动力学行为.By establishing a class of stochastic AIDS infectious disease model,the unique-ness of the global existence of the positive solution of the stochastic model is proved by using the stop-time theory Secondly,the oscillation behavior of the solution of the stochastic model near the disease-free equilibrium point and the endemic equilibrium point of the correspond-ing deterministic model is analyzed,and the suficient conditions for the average persistence and extinction of the stochastic model solution are obtainedFinally,the dynamic behavior of the model is further demonstrated by numerical simulation.

关 键 词：随机模型 伊藤公式 渐近行为 持久性 灭绝性 

分 类 号：R512.91[医药卫生—内科学] O211.6[医药卫生—临床医学]