Deterministic Site Exchange Cellular Automata Models for the Spread of Diseases in Human Settlements
Ricardo Mansilla
Center for Interdisciplinary Research in Science and the Humanities,
National University of Mexico
and
Faculty of Mathematics and Computer Science,
University of Havana, Cuba
José L. Gutierrez
Agroecological Program,
Chapingo University,
Chapingo, Mexico
Abstract
A cellular automata model that describes as limit cases the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Realistic assumptions in the motion of human populations are considered. A parameter describing the range of that motion is defined. For small (large) values of this parameter, the behavior described by partial (ordinary) differential equation models are reproduced. Emphasis is also placed on the study of those scenarios which the differential equations fail to describe. In the study of these cases some interesting results, including evidence of period doubling behavior, are reported.
