Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations.
Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations.
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DOI：
10.1515/crll.1979.306.94
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发表时间：
1979-03
期刊：
影响因子：
--
通讯作者：
H. Thieme
中科院分区：
文献类型：
--
作者：
H. Thieme
最近，Aronson [1]将他和Weinberger [3]，[4]为种群遗传学，燃烧和神经传播中的非线性扩散问题开发的渐近速度概念扩展到Kendall [11]，[12]在1957年（1965年）提出的流行病模型。在这个模型中（这是Kermack和McKendrick流行病模型的空间版本[13]），感染的个体立即变得具有传染性，并以恒定的速度被移除。该模型没有考虑到，大多数传染病的感染者在感染之前都有一个潜伏期，而且他们只在一段固定的时间内保持感染性。这些特征不能用Aronson [1]考虑的方程来描述，该方程包含关于时间的导数和关于空间的积分。因此，希望将Aronson和Weinberger的渐近速度概念推广到非线性积分方程t J g（u（t-s，x+y））k（s9\y\）dsdy
Recently Aronson [1] extended the concept of asymptotic speed which he and Weinberger [3], [4] had developed for nonlinear diffusion problems in population genetics, combustion and nerve propagation, to an epidemic model proposed by Kendall [11], [12] in 1957 (1965). In this model (which is a spatial version of Kermack's and McKendrick's epidemic model [13]) the aflfected individuals become immediately infectious and are removed at a constant rate. The model does not take into account that with most infectious diseases the affected individuals underlie an incubation period, before they become infective, and that they remain infective for a fixed period only. These features cannot be described by the equation considered by Aronson [1] which contains a derivative with respect to time and an integral with respect to space. It is therefore desirable to extend Aronson's and Weinberger's concept of asymptotic speed to the nonlinear integral equation t J g(u(t-s,x+y))k(s9\y\)dsdy