一类具有季节变化和周期解的随机SIR传染病模型  

Periodic Solution of a Stochastic SIR Epidemic Model with Seasonal Variation

作　　者：王来全[1] 夏米西努尔·阿布都热合曼[2] WANG Laiquan;Xamxinur Abdurahman(Department of Basic Courses,Changji Vocational and Technical College,Changji 831100,China;College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]昌吉职业技术学院基础部,新疆昌吉831100 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《北华大学学报（自然科学版）》2020年第5期568-572,共5页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(11861063);昌吉职业技术学院教科研项目(CJZY2020002).

摘　　要：考虑了一类具有季节变化的随机SIR传染病模型,得到决定疾病流行与否的阈值,讨论了疾病的灭绝与持久性,在疾病持久的条件下,证明了模型存在一个非平凡正周期解.We consider a stochastic SIR epidemic model with seasonal variation and obtain the threshold of model which determines whether the epidemic occurs or not,discuss that the disease is extinction and persistence in the population,we prove that there is a nontrivial positive periodic solution under conditions of persistence.

关 键 词：季节变化 随机模型 灭绝和持久 周期解 

分 类 号：O175.1[理学—数学]