Research Article
SIRS Dynamics on Random Networks: Simulations and Analytical Models
@INPROCEEDINGS{10.1007/978-3-642-02466-5_78, author={Ganna Rozhnova and Ana Nunes}, title={SIRS Dynamics on Random Networks: Simulations and Analytical Models}, proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009. Revised Papers, Part 1}, proceedings_a={COMPLEX PART 1}, year={2012}, month={5}, keywords={stochastic epidemic models oscillations pair approximations random regular graphs}, doi={10.1007/978-3-642-02466-5_78} }- Ganna Rozhnova
Ana Nunes
Year: 2012
SIRS Dynamics on Random Networks: Simulations and Analytical Models
COMPLEX PART 1
Springer
DOI: 10.1007/978-3-642-02466-5_78
Abstract
The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree 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 and of its relevance to understand the behaviour of simulations on networks. For = 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.