具有标准发生率及饱和治疗函数的随机SIS传染病模型的灭绝性和持久性  

Extinction and Persistence of a Stochastic SIS Epidemic Model with Standard Incidence and Saturated Treatment Functions

作　　者：谭杨[1] 杨林 郭子君[2] TAN Yang;YANG Lin;GUO Zijun(School of Information Engineering,Tongren Polytechnic College,Tongren 554300,China;Institute of Applied Mathematics,South-China Agricultural University,Guangzhou 510642,China)

机构地区：[1]铜仁职业技术学院信息工程学院,贵州铜仁554300 [2]华南农业大学应用数学研究所,广东广州510642

出　　处：《中北大学学报(自然科学版)》2025年第2期245-253,共9页Journal of North University of China(Natural Science Edition)

摘　　要：研究了一类具有标准发生率和饱和治疗函数的随机易感-感染-易感(SIS)传染病模型。首先,利用构造李雅普诺夫函数方法证明了模型正解的存在、唯一性。然后,在灭绝性方面得到了感染种群趋于普通灭绝和依指数灭绝的充分条件,其结果表明,随机基本再生数小于1时,感染种群必将趋于灭绝,而依指数灭绝则需要更强的条件。在持久性方面,得到了感染种群趋于依平均持久和随机持久的充分条件,其结果表明,随机基本再生数大于1时,感染种群随机持久,而依平均持久需要更强的条件才能满足。最后,通过数值模拟进行了结果验证。A stochastic susceptibility infection-susceptibility(SIS)epidemic model with standard incidence and saturated treatment function was studied.Firstly,the existence and uniqueness of the positive solution of the model were proved by constructing Lyapunov function.Then,in terms of extinction,the sufficient conditions for the infected population to tend to general extinction and exponential extinction were obtained.The results show that the infected populations will tend to extinction when the stochastic basic reproduction number is less than 1,while the exponential extinction requires stronger conditions.In terms of persistence,sufficient conditions were obtained for the persistence in the mean and stochastic persistence of the infected population.The results show that the infected populations are stochastically persistent when the stochastic basic reproduction number is greater than 1,while the persistence in the mean required stronger conditions.Finally,numerical simulation was given to prove the research results.

关 键 词：SIS模型 标准发生率 饱和治疗函数 灭绝性 持久性 

分 类 号：O211.63[理学—概率论与数理统计]