Periodic Traveling Wave Solutions of Time-Periodic SIR Epidemic Models With External Supplies
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摘要:
研究了一类带有外部输入项的时间周期SIR传染病模型周期行波解的存在性和不存在性。首先，通过构造辅助系统适当的上下解并定义闭凸锥，将周期行波解的存在性转化为定义在这个闭凸锥上的非单调算子的不动点问题，利用Schauder不动点定理建立辅助系统周期解的存在性，并利用Arzela-Ascoli定理证明了原模型周期行波解的存在性。其次，借助分析技术得到了周期行波解的不存在性。
Abstract:The existence and non-existence of periodic traveling wave solutions of a class of time-periodic SIR epidemic models with external supplies were considered. Firstly, the appropriate upper and lower solutions of the auxiliary system were built and a closed convex cone was defined, the existence of periodic traveling waves was transformed into a fixed-point problem of the non-monotonic operator defined on the closed convex cone. The existence of periodic solutions of the auxiliary system was established under the Schauder fixed-point theorem, and the Arzela-Ascoli theorem was used to prove the existence of periodic traveling waves for the original model. Secondly, the non-existence of periodic traveling waves was obtained by analytic techniques.
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Key words:
- periodic traveling wave solution /
- existence /
- auxiliary system /
- fixed-point theorem
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