Individually based SIR models, their motivation, and their spatio-temporal dynamics

We describe traditional epidemics' modeling methodologies. We identify the need for and outline individually based methodologies. We describe a model based on the LGCA (Lattice Gas Cellular Automata) methodology and EpiLab, the software package that we developed to simulate our model. Finally, we present an individually based fully discrete simulation model to study spatio-temporal dynamics of spread of epidemics of SIR (susceptible-infectious-removed) type, i.e. influenza epidemics. In our model number of individuals, space and time are discrete variables. We investigate effects of spatial heterogeneities in distribution of infected and vaccinated individuals on the dynamics of SIR type epidemics. We discuss vaccination strategies that differ only in spatial distribution of vaccinated individuals. We study the role of mixing of individuals on the spread of epidemics of SIR type in realistic population distribution of Southern and Central Ontario using census data obtained from Statistics Canada. We present various simulation results. Our work is of relevance to study epidemics of SIR type including influenza epidemics.