Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 137854, 10 pages
doi:10.1155/2009/137854
Research Article

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

L. H. A. Monteiro,1,2 D. N. Oliveira,1 and J. G. Chaui-Berlinck3

1Pós-graduação em Engenharia Elétrica, Escola de Engenharia, Universidade Presbiteriana Mackenzie, Rua da Consolação, n.896, 01302-907 São Paulo, SP, Brazil
2Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica, Universidade de São Paulo, Avendia Professor Luciano Gualberto, travessa 3, n.380, 05508-900 São Paulo, SP, Brazil
3Departamento de Fisiologia, Instituto de Biociências, Universidade de São Paulo, Rua do Matão, travessa 14, n.321, 05508-900 São Paulo, SP, Brazil

Received 28 October 2008; Revised 2 February 2009; Accepted 23 February 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 L. H. A. Monteiro et al. 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.

Abstract

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented.