Spreading disease: integro-differential equations old and new.

TitleSpreading disease: integro-differential equations old and new.
Publication TypeJournal Article
Year of Publication2003
AuthorsMedlock J, Kot M
JournalMathematical biosciences
Volume184
Issue2
Pagination201-22
Date Published2003 Aug
ISSN0025-5564
KeywordsCommunicable Diseases, Disease Transmission, Infectious, Epidemiologic Methods, Humans, Models, Biological, Models, Statistical, Numerical Analysis, Computer-Assisted
Abstract

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.

Alternate JournalMath Biosci