%0 Journal Article %1 mollison1977spatial %A Mollison, Denis %D 1977 %I Blackwell Publishing for the Royal Statistical Society %J Journal of the Royal Statistical Society. Series B (Methodological) %K contact_process epidemic long_distance_dispersal spatial_spread travelling_wave %N 3 %P 283--326 %T Spatial Contact Models for Ecological and Epidemic Spread %U http://www.jstor.org/stable/2985089 %V 39 %X A wide variety of phenomena of geographical spread can be described in terms of a mechanism of "growth" (e.g. birth, infection) and a "contact distribution" which describes how the locations of the individual(s) involved in a migratory move, or infection at a distance, are spatially related. I shall survey work on such models, beginning with an examination of the relations between stochastic and deterministic models; it emerges that both linear and nonlinear deterministic models have close connections with the less interesting "linear" (exponential growth) stochastic models. More realistic models must be nonlinear as well as stochastic; some results are now available for such models. As in the linear case, these deal mainly with asymptotic behaviour. Simulations reveal that nonlinear stochastic processes have a richer spectrum of non-asymptotic behaviour than linear models, though in some circumstances the simpler models may provide an adequate approximation. Thus theoretical study of the short-term behaviour of such processes may be difficult, but should prove rewarding. The other main outstanding problems are those of inference for such models, especially the estimation of contact distributions.

@article{mollison1977spatial, abstract = {A wide variety of phenomena of geographical spread can be described in terms of a mechanism of "growth" (e.g. birth, infection) and a "contact distribution" which describes how the locations of the individual(s) involved in a migratory move, or infection at a distance, are spatially related. I shall survey work on such models, beginning with an examination of the relations between stochastic and deterministic models; it emerges that both linear and nonlinear deterministic models have close connections with the less interesting "linear" (exponential growth) stochastic models. More realistic models must be nonlinear as well as stochastic; some results are now available for such models. As in the linear case, these deal mainly with asymptotic behaviour. Simulations reveal that nonlinear stochastic processes have a richer spectrum of non-asymptotic behaviour than linear models, though in some circumstances the simpler models may provide an adequate approximation. Thus theoretical study of the short-term behaviour of such processes may be difficult, but should prove rewarding. The other main outstanding problems are those of inference for such models, especially the estimation of contact distributions.}, added-at = {2009-12-02T23:24:12.000+0100}, author = {Mollison, Denis}, biburl = {https://www.bibsonomy.org/bibtex/21040db92189e6d3991da89ede9efcd1b/peter.ralph}, copyright = {Copyright © 1977 Royal Statistical Society}, interhash = {e6dd6304db90ab9ea04166b56e23b382}, intrahash = {1040db92189e6d3991da89ede9efcd1b}, issn = {00359246}, journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, jstor_articletype = {primary_article}, jstor_formatteddate = {1977}, keywords = {contact_process epidemic long_distance_dispersal spatial_spread travelling_wave}, number = 3, pages = {283--326}, publisher = {Blackwell Publishing for the Royal Statistical Society}, timestamp = {2013-09-12T22:23:01.000+0200}, title = {Spatial Contact Models for Ecological and Epidemic Spread}, url = {http://www.jstor.org/stable/2985089}, volume = 39, year = 1977 }