两类非局部扩散传染病系统的行波解 Alternative Title Travelling Waves of Two Kinds of Epidemic Systems with Nonlocal Dispersal 乔润陇 Thesis Advisor 李万同 2013-05-23 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 非局部扩散 传染病系统 行波解 上下解 双边Laplace变换 不动点 时空时滞 阈值 Abstract 本文讨论了两类具有全局扩散效应的传染病系统，分别使用不同的方法得到其行波解存在性的条件。首先，研究了卡帕索-马达莱纳非局部扩散传染病系统。将系统波前解的存在性问题减弱为一个方程单调解存在性的问题，继而利用上下解结合单调迭代的方法证明其波前解的存在性。作为推广，考虑了已感者对病原体的非局部作用，得到了一个更为复杂的系统，并用上述方法对其波前解进行了研究，得到了类似的结论。进一步，考虑了病原体的扩散、非局部作用（包括病原体之间、已感者与病原体之间）对临界波速的影响。其次，考虑了具有时空时滞的非局部扩散克马克-麦肯德里克传染病系统（即SIR传染病系统）。当波速大于临界波速时，通过在一个有界的闭凸不变锥上构造全连续算子，把证明系统存在行波解转化为证明该算子在不变锥上存在不动点，继而利用肖德尔不动点定理解决了这一问题；当波速为正且小于临界波速时，使用双边拉普拉斯变换证明了该系统不存在行波解；此外还得到了决定传染病传播与否的阈值条件，并讨论了随机移动、非局部作用和时滞对临界波速（也即行波解的最小波速）的影响。 Other Abstract First, the Capasso-Maddalena epidemic system with nonlocal dispersal is studied. The existence of travelling wavefronts are obtained by using the super-lower solution technique combined with monotone iteration.. Furthermore, a complicated system including the nonlocal effect from infected individual to infectious agent is discussed by means of the method mentioned above. Second, the SIR epidemic system with nonlocal dispersal and spatio-temporal delay is considered. When c>c*(c* denotes the critical speed of travelling wave), we use Schauder's fixed point theorem to obtain the existence of travelling wave solutions. When c*>c>0, the non-existence of travelling wave solution is proved by using two-sided Laplace transform. Furthermore, threshold value determining whether epidemic disease can spread or not is obtained, the effect of spatial heterogeneity,nonlocal interaction and time delay on c* are also considered. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224903 Collection 数学与统计学院 Recommended CitationGB/T 7714 乔润陇. 两类非局部扩散传染病系统的行波解[D]. 兰州. 兰州大学,2013.
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