Medlock Jan, Kot Mark
Department of Applied Mathematics, University of Washington, PO Box 352420, Seattle, WA 98195-2420, USA.
Math Biosci. 2003 Aug;184(2):201-22. doi: 10.1016/s0025-5564(03)00041-5.
We investigate an integro-differential equation for a disease spread by the dispersal of infectious individuals and compare this to Mollison's [Adv. Appl. Probab. 4 (1972) 233; D. Mollison, The rate of spatial propagation of simple epidemics, in: Proc. 6th Berkeley Symp. on Math. Statist. and Prob., vol. 3, University of California Press, Berkeley, 1972, p. 579; J. R. Statist. Soc. B 39 (3) (1977) 283] model of a disease spread by non-local contacts. For symmetric kernels with moment generating functions, spreading infectives leads to faster traveling waves for low rates of transmission, but to slower traveling waves for high rates of transmission. We approximate the shape of the traveling waves for the two models using both piecewise linearization and a regular-perturbation scheme.
我们研究了一个关于通过感染个体的扩散来传播疾病的积分 - 微分方程，并将其与莫利森[《应用概率进展》4 (1972) 233；D. 莫利森，《简单流行病的空间传播速率》，载于：《第六届伯克利数学统计与概率研讨会论文集》，第3卷，加利福尼亚大学出版社，伯克利，1972年，第579页；《皇家统计学会会刊B》39 (3) (1977) 283]的通过非局部接触传播疾病的模型进行比较。对于具有矩生成函数的对称核，在低传播速率下，感染个体的扩散会导致更快的行波，但在高传播速率下会导致更慢的行波。我们使用分段线性化和正则摄动方案来近似这两个模型的行波形状。
