一类具有非线性传染率、隔离率的SIRS传染病模型解的存在性研究

Study on the Existence of Solution to an SIRS Epidemic Model with Nonlinear Contact and Screening Rates

染病年龄结构数学模型已经成为应用数学领域的研究热点之一.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.在形式上,这类模型是常微分方程和偏微分方程相结合的微分方程组.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和应用价值,正被广大学者关注.建立了具有一般非线性接触率、一般非线性隔离率及染病年龄结构SIRS传染病模型并综合运用Bellman-Gronwall引理、不动点定理及解的延拓定理等多种数学方法证明模型全局非负解的存在性及惟一性.

One of study focuses in applied mathematics is the mathematical model of infection-age dependence which is more appropriate for infections diseases with long infection-age such as AIDs,etc,since the incidence rate is dependent on infection-age.The model consists of combined system of ordinary and partial differential equations.The existence and uniqueness of solution to the system have been taken with theoretical significance and applicable value.In the present paper,an SIRS epidemic model with general nonlinear contact rate,general screening rate and infection-age dependence is first formulated.Then,by using the mathematical methods of Bellman-Gronwall lemma,the fixed point theorem,the extension thoerem,and so on,the existence and uniqueness of the globally non-negative solultion are discussed.