RUN FOR YOUR LIFE - NOTE ON THE ASYMPTOTIC SPEED OF PROPAGATION OF AN EPIDEMIC
RUN FOR YOUR LIFE - NOTE ON THE ASYMPTOTIC SPEED OF PROPAGATION OF AN EPIDEMIC
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DOI：
10.1016/0022-0396(79)90080-9
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发表时间：
1979-01-01
影响因子：
2.4
通讯作者：
DIEKMANN, O
中科院分区：
文献类型：
--
作者：
DIEKMANN, O
研究了一类描述流行病时空发展的混合Volterra-Fredholm型非线性积分方程解的大时间性态。对于这个模型，我们知道存在一个最小波速c0(即当c？>；c0时存在速度为c的行波解，而当？c？<；c0时则不存在)。本文证明了c0是传播的渐近速度(即对任意c1，c2具有0<；c1<；c0<；c0<；c2的解在x？⩾c2 t区域内一致趋于零，但在t足够大时，它在x？⩽c1 t区域一致远离零).
We study the large-time behaviour of the solution of a nonlinear integral equation of mixed Volterra-Fredholm type describing the spatio-temporal development of an epidemic. For this model it is known that there exists a minimal wave speed c 0 (ie, travelling wave solutions with speed c exist if¦ c¦> c 0 and do not exist if¦ c¦< c 0). In this paper we show that c 0 is the asymptotic speed of propagation (ie, for any c 1, c 2 with 0< c 1< c 0< c 2 the solution tends to zero uniformly in the region¦ x¦⩾ c 2 t, whereas it is bounded away from zero uniformly in the region¦ x¦⩽ c 1 t for t sufficiently large).