Travelling wave solutions for an infection-age structured epidemic model with external supplies
Travelling wave solutions for an infection-age structured epidemic model with external supplies
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DOI：
10.1088/0951-7715/24/10/012
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发表时间：
2011-09
期刊：
影响因子：
1.7
通讯作者：
A. Ducrot;Pierre Magal
中科院分区：
文献类型：
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作者：
A. Ducrot;Pierre Magal
本文的目的是探讨某些传染病的空间侵入性。通过自感染以来的年龄来描述污染过程。与经典的Kermack和McKendrick模型相比，该模型没有忽略生命动力学，并且允许一定的输入通量进入种群。在流行病问题的背景下，这个问题是相当自然的，而且还没有被研究过。在这里，我们证明了行波解的存在性和不存在性结果。我们还描述了最小波速。我们能够构造一个合适的李雅普诺夫函数沿沿着减少允许导出一些定性的性质，即他们的收敛到平衡点在x = ±∞。
The aim of this paper is to investigate the spatial invasion of some infectious disease. The contamination process is described by the age since infection. Compared with the classical Kermack and McKendrick's model, the vital dynamic is not omitted, and we allow some constant input flux into the population. This problem is rather natural in the context of epidemic problems and it has not been studied. Here we prove an existence and non-existence result for travelling wave solutions. We also describe the minimal wave speed. We are able to construct a suitable Lyapunov like functional decreasing along the travelling wave allowing to derive some qualitative properties, namely their convergence towards equilibrium points at x = ±∞.