Discrete Dynamics in Nature and Society
Volume 6 (2001), Issue 3, Pages 191-200

Individual-based lattice model for spatial spread of epidemics

Henryk Fukś3,4 and Anna T. Lawniczak1,2,3

1Department of Mathematics and Statistics, University of Guelph, Ontario, Guelph N1G 2W1, Canada
2Guelph-Waterloo Institute of Physics, University of Guelph, Ontario, Guelph N1G 2W1, Canada
3The Fields Institute for Research in Mathematical Sciences, Ontario, Toronto M5T 3J1, Canada
4Department of Mathematics, Brock University, St. Catharines Ont L2S3A1, Canada

Received 25 June 2000

Copyright © 2001 Henryk Fukś and Anna T. Lawniczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e., space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean-field type description of the automaton, and discuss differences between the mean-field dynamics and the results ofLGCA simulation.