Discrete Dynamics in Nature and Society
Volume 6 (2001), Issue 3, Pages 191-200
doi:10.1155/S1026022601000206
Individual-based lattice model for spatial spread of epidemics
Henryk Fukś1
and Anna T. Lawniczak2
1The Fields Institute for Research in Mathematical Sciences, Ontario, Toronto M5T 3J1, Canada
2Department of Mathematics and Statistics, University of Guelph, Ontario, Guelph N1G 2W1, Canada
Abstract
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.