Pair Approximation for Models of Disease Spread

Details Pair Approximation for Models of Disease Spread Pair Approximation for Models of Disease Spread

2005-10-03

arxiv.org/abs/q-bio/0510005v4

Eur. Phys. J. B 50 (2006), no. 1-2, 177--181

Biology

Quantitative Biology

Populations and Evolution

6 pages, 3 figures, LaTeX2e+SVJour+AmSLaTeX, NEXTSigmaPhi 2005

Scientific paper

10.1140/epjb/e2006-00096-x

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.

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