具一般非线性接触率、隔离和染病年龄结构的SIQS模型非负解的存在惟一性  

The Existence and Uniqueness of the Non-negative Solution to an SIQS with Nonlinear Concant Rate,Quarantine and Infection-age

作　　者：王晓凤[1] 段志霞[2] 

机构地区：[1]河南城建学院数理系,河南平顶山467044 [2]济源职业技术学院基础部,河南济源454650

出　　处：《四川师范大学学报（自然科学版）》2012年第1期43-48,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：河南省科技厅基金(10400450243)资助项目

摘　　要：染病年龄的引入使传染率依赖于染病年龄,这样所建立的模型更适合染病期较长的疾病,如AIDS等.而且从形式上讲,模型是常微分方程和偏微分方程相结合的微分方程模型.对这类模型非负解存在性及惟一性研究具有重要的理论意义,正被广大学者关注.首先,将SIQS传染病模型引入了一般非线性接触率及染病年龄结构建立了一类新的SIQS传染病模型,继而综合运用Bellman-Grownall引理、不动点定理讨论模型非负解的存在性及惟一性,最后由延拓方法将解延拓到正半实数轴.Introducing the notion of infection-age makes the incidence rate dependent on infection-age.The model established in this way is more suitable for epidemic diseases with long infection-ages such as AIDS.The form of the model is ordinary of partial differential equation.The existence and uniqueness of non-negative solution play an important role in study of this model.In this paper,a new mathematical model is formulated by introducing general nonlinear contact-rate and infection-age structure into the SIQS model proposed by Hethcote.The existence and uniqueness of non-negative solution to it is proved by using Bellman-Grownall Lemma and the fixed point theorem.It is also proved that the solution can be extended to the positive half axis.

关 键 词：隔离 非线性接触率 染病年龄 SIQS传染病模型 非负解 

分 类 号：O175[理学—数学]