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Spreading disease: integro-differential equations old and new.
|Title||Spreading disease: integro-differential equations old and new.|
|Publication Type||Journal Article|
|Year of Publication||2003|
|Authors||Medlock J, Kot M|
|Date Published||2003 Aug|
|Keywords||Communicable Diseases, Disease Transmission, Infectious, Epidemiologic Methods, Humans, Models, Biological, Models, Statistical, Numerical Analysis, Computer-Assisted|
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 Journal||Math Biosci|