%0 Journal Article %1 medlock2003spreading %A Medlock, Jan %A Kot, Mark %D 2003 %J Mathematical Biosciences %K disease_outbreak integro-difference travelling_wave %N 2 %P 201 - 222 %R DOI: 10.1016/S0025-5564(03)00041-5 %T Spreading disease: integro-differential equations old and new %U http://www.sciencedirect.com/science/article/B6VHX-48CNVKJ-1/2/898e1dc4b6ee83834c922721d4cfa166 %V 184 %X 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.

@article{medlock2003spreading, 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.}, added-at = {2010-01-18T19:58:04.000+0100}, author = {Medlock, Jan and Kot, Mark}, biburl = {https://www.bibsonomy.org/bibtex/28eb5729cead415f2bd77e58c0d4744a2/peter.ralph}, description = {ScienceDirect - Mathematical Biosciences : Spreading disease: integro-differential equations old and new}, doi = {DOI: 10.1016/S0025-5564(03)00041-5}, interhash = {926e45a5f10d43e6b1bcdd8818e4113b}, intrahash = {8eb5729cead415f2bd77e58c0d4744a2}, issn = {0025-5564}, journal = {Mathematical Biosciences}, keywords = {disease_outbreak integro-difference travelling_wave}, number = 2, pages = {201 - 222}, timestamp = {2013-09-12T22:23:01.000+0200}, title = {Spreading disease: integro-differential equations old and new}, url = {http://www.sciencedirect.com/science/article/B6VHX-48CNVKJ-1/2/898e1dc4b6ee83834c922721d4cfa166}, volume = 184, year = 2003 }