Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2008-12-09
Complex Sciences: Complex 2009, Part I, LNICST 4, edited by J. Zhou (Springer Berlin Heidelberg, 2009), pp. 792-797
Biology
Quantitative Biology
Populations and Evolution
6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, China
Scientific paper
10.1007/978-3-642-02466-5_78
The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.
Nunes A. A.
Rozhnova Ganna
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