Markov切换模式下双疾病随机SIRS模型的稳定性分析  

Stability analysis for a stochastic SIRS model of double diseases under Markov switching mode

作　　者：肖思佳 张靖文 林萍芝 王浩华 Xiao Sijia;Zhang Jingwen;Lin Pingzhi;Wang Haohua(School of Sciences,Hainan University,Haikou 570228,China;Hainan Key Laboratory for engineering modeling and statisti-cal calculation,Haikou 570228,China;Ministry of Education Key Laboratory for Genetics&Germplasm Enhancement of Tropical Specialty Forest and Flowers and Plants,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228 [2]海南大学海南省工程建模与统计计算重点实验室,海南海口570228 [3]海南大学热带特色林木花卉遗传与种质创新教育部重点实验室,海南海口570228

出　　处：《海南大学学报（自然科学版）》2023年第4期343-351,共9页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(12261028,11961018);海南省自然科学基金(120RC451,2019RC168);海南省重点研发项目(ZDYF2021SHFZ231);海南省研究生创新创业项目(Qhys2021⁃208)。

摘　　要：研究了一类在Markov切换下具有不同发生率的双疾病随机SIRS传染病模型.首先,利用伊藤公式构造了新的Lyapunov函数,证明系统全局正解的存在唯一性,并得到了系统动力学的相关阈值.当阈值满足相关条件,系统具有唯一平稳分布且是遍历的,且得到了疾病灭绝与持久的阈值条件,探讨了环境变化对疾病的影响,结果表明噪声在一定条件下能够使疾病灭绝,最后通过数值模拟验证了结论的正确性.In the report,a stochastic SIRS epidemic model with different incidence for double disease under Mar-kov switching mode was constructed.Firstly,Ito's formula was used to construct Lipaunov function,and the threshold dynamic of the system was derived.The results indicated that if the threshold is greater than 1,the system is ergodic and the disease converge to zero.Moreover,the effects of the environment on disease were fur-ther analyzed.The results showed that the noise can accelerate the disease extinction under some special condi-tions,and which are verified by the numerical simulation.

关 键 词：Markov切换 随机传染病模型 双疾病 灭绝性 持久性 

分 类 号：R181[医药卫生—流行病学] O232[医药卫生—公共卫生与预防医学]