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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

, PP. 482-489

Keywords: 隔离率,接触率,SIRS传染病模型,染病年龄

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Abstract:

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.

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