一类离散SIRS传染病模型的持久性  

Persistence of a Class of Discrete SIRS Epidemic Model

作　　者：赵爱民[1] 李文娟[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2016年第1期24-30,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11471197);山西省自然科学基金(2014011005-1)

摘　　要：考虑具有非线性发病率及分布时滞h∑k=0Pkf(Sn+1,In-k)的离散SIRS模型,利用差分不等式理论得到模型持久性的充分条件。当f(x,y)=βxG(y)时,对应模型持久的充分条件为:G(y)在[0,∞)连续单增,G(0)=0,函数G(y)/y在(0,∞)单减有界。该结论改进了[生物数学学报,2013,38(2):274-259]中的相关结论。当易感者输入率等于死亡率时,本文结论是[Appl Math Comput,2012,39:15-34]中定理4.1的离散化形式。This paper considers the discrete SIRS model with nonlinear incidence rates and distributed delay f（x,y）=βxG（y） k=OThe sufficient conditions for the persistence of the model are obtained by using differ-ence inequality. When f（x,y）=flxG（y）,the corresponding sufficient conditions are that G（y） is continuous and nondeereasing on [0,∞）,G（y）/y is bounded and nonincreasing on （0,∞） and G（O）=0. This re-sult extends and improves the corresponding result on [Journal of Biomathematics,2013,28（2）：247-259]. If the birth rate of susceptible is equal to the death rate of susceptible,then the conclusion of this paper is discrete form of theorem 4.1 of [Appl Math Comput,2012,39：15-34].

关 键 词：分布时滞 持久性 SIRS模型 

分 类 号：O175[理学—数学]