Small-World Effect in Epidemics Using Cellular Automata

Abstract

The spread of an infectious disease in a population involves interactions leading to an epidemic outbreak through a network of contacts. Extending on Watts and Strogatz (1998) who showed that short-distance connections create a small-world effect, a model combining short- and long-distance probabilistic and regularly updated contacts helps considering spatial heterogeneity. The method is based on cellular automata. The presence of long-distance connections accelerates the small-world effect, as if the world shrank in proportion of their total number.

Keywords:

• automata cellular
• epidemic spreading
• SIR
• SIRS
• small-world
• transmission rules

ACKNOWLEDGMENTS

This work was supported in part by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (Proc. 02/03564-8). We thank the anonymous reviewer for helpful comments.