潜伏期和染病期均具有传染性的媒介传染病模型的全局稳定性分析(英文)  

Global Analysis of a Host-vector Model with Infectious Force in Latent and Infected Period

作　　者：Abid Ali Lashari Muhammad Ozair Gul Zaman 李学志[3] 

机构地区：[1]Centre for Advanced Mathematics and Physics,National University of Sciences and Technology H-12Islamabad,Pakistan [2]Department of Mathematics,University of Malakand Chakdara Dir(Lower) Khyber Pukhtoonkhwa,Pakistan [3]信阳师范学院 数学学院,信阳464000

出　　处：《应用泛函分析学报》2012年第4期321-329,共9页Acta Analysis Functionalis Applicata

基　　金：Supported by the NSF of China(10971178)

摘　　要：讨论潜伏期和染病期均具有传染性的媒介传染病模型.得到模型基本再生数的表达式,证明了当基本再生数小于1时,无病平衡点是全局渐近稳定的,此时疾病消亡;当基本再生数大于1时,无病平衡点是不稳定的,系统存在全局渐近稳定的地方病平衡点,此时,疾病将在人群中持续存在,数值模拟验证了理论结果.In this paper,a mathematical model to study the dynamics of a vector-borne disease is discussed.The global stability of epidemic equilibrium and disease-free equilibrium is proved.The basic reproduction number is derived,thresholds conditions for the elimination of the disease are identified.The disease-free equilibrium solution of the system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one and the disease will be cleared out of the host.We established that a unique endemic equilibrium is globally stable in the interior of a feasible region and the disease persists at the endemic steady state when the basic reproduction number is larger than one.

关 键 词：媒介传染病模型 平衡点 全局稳定性 

分 类 号：R74[医药卫生—神经病学与精神病学] R73[医药卫生—临床医学]