ANALYSIS OF AN EPIDEMIC MODEL WITH CROWLEY-MARTIN INCIDENCE RATE AND HOLLING TYPE Ⅱ TREATMENT  

作　　者：Liuqing Yang Fengying Wei 

机构地区：[1]College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,Fujian,PR China [2]Key Laboratory of Operations Research and Control of Universities in Fujian,Fuzhou University,Fuzhou 350108,Fujian,PR China

出　　处：《Annals of Applied Mathematics》2020年第2期204-220,共17页应用数学年刊（英文版）

基　　金：supported by NSFC under grants 11201075 and 11601085。

摘　　要：We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type Ⅱ treatment,where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.

关 键 词：epidemic model Crowley-Martin incidence rate EXTINCTION PERSISTENCE 

分 类 号：O175[理学—数学] R181[理学—基础数学]