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A Spatial Epidemic Model with Site Contamination
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-9228-7357
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32018 (English)In: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 24, no 1, p. 25-38Article in journal (Refereed) Published
Abstract [en]

We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process supercritical. Each site on Z(d) is independently assigned a random number of particles and these then perform random walks restricted to bounded regions around their home locations. At time 0, the origin is infected along with all its particles. The infection then spread in that an infected particle that jumps to a new site causes the site along with all particles located there to be infected. Also, a healthy particle that jumps to a site where infection is present, either in that the site is infected or in the presence of infected particles, becomes infected. Particles and sites recover at rate lambda and gamma, respectively, and then become susceptible to the infection again. We show that, for each given value of lambda, there is a positive probability that the infection survives indefinitely if gamma is sufficiently small, and that, for each given value of gamma, the infection dies out almost surely if lambda is large enough. Several open problems and modifications of the model are discussed, and some natural conjectures are supported by simulations.

Place, publisher, year, edition, pages
2018. Vol. 24, no 1, p. 25-38
Keywords [en]
spatial epidemic, interacting particle system, phase transition, critical value
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-160292ISI: 000440875300003OAI: oai:DiVA.org:su-160292DiVA, id: diva2:1248939
Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2019-12-17Bibliographically approved

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