一类具有饱和发生率和环境感染的传染病模型的稳定性  

Stability of epidemic model with saturation incidence and environmental infection

作　　者：郝艳荣 赵春[1] HAO Yanrong;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2023年第2期17-22,共6页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高等学校创新团队培养计划资助项目(TD13-5078).

摘　　要：讨论一类具有饱和发生率和环境感染的传染病模型的稳定性.利用下一代矩阵法得到了基本再生数R0的表达式.当R0<1时,通过构造Lyapunov函数并利用LaSalle不变集原理,证明了模型在无病平衡点处全局渐近稳定;当R0>1时,证明了地方病平衡点存在且唯一.最后,通过数值模拟验证无病平衡点的稳定性,并分析疫苗接种率对基本再生数的影响.The stability of a epidemic model with saturation incidence and environmental infection is discussed.The expression of basic reproduction number R0 is obtained by using the next-generation matrix method.When R0<1,the global asymptotic stability of the system at the disease-free equilibrium is proved by constructing Lyapunov function and using LaSalle′s invariance principle.When R0>1,it is proved that the system exists a unique endemic equilibrium.Finally,the stability of disease-free equilibriummain is verified and the effect of vaccination rate on the basic reproduction number is analyzed by numerical simulation.

关 键 词：基本再生数 平衡点 稳定性 饱和发生率 

分 类 号：O175[理学—数学]