Pair approximation models for disease spread

J. Benoit (), A. Nunes and M. Telo da Gama

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 50, issue 1, 177-181

Abstract: We consider a Susceptible-Infective-Recovered ( SIR) model, where the mechanism for the renewal of susceptibles is demographic, on a ring with next nearest neighbour interactions, and a family of correlated pair approximations ( CPA), parametrized by a measure of the relative contributions of loops and open triplets of the sites involved in the infection process. We have found that the phase diagram of the CPA, at fixed coordination number, changes qualitatively as the relative weight of the loops increases, from the phase diagram of the uncorrelated pair approximation to phase diagrams typical of one-dimensional systems. In addition, we have performed computer simulations of the same model and shown that while the CPA with a constant correlation parameter cannot describe the global behaviour of the model, a reasonable description of the endemic equilibria as well as of the phase diagram may be obtained by allowing the parameter to depend on the demographic rate. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 02.50.-r Probability theory; stochastic processes; and statistics; 87.23.Ge Dynamics of social systems; 05.70.Ln Nonequilibrium and irreversible thermodynamics (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00096-x

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