SIRS dynamics on random networks: simulations and analytical models

Abstract

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.

6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, China

References in corpus (5)

• Rock-scissors-paper game on regular small-world networks
• Stochastic Lattice Gas Model for a Predator-Prey System
• Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice
• Pair Approximation Models for Disease Spread
• Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach

Cited by in corpus (6)

• Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
• Fluctuations and oscillations in a simple epidemic model
• Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model
• Collective oscillations of excitable elements: order parameters, bistability and the role of stochasticity
• Collective behavior of coupled nonuniform stochastic oscillators
• Population dynamics on random networks: simulations and analytical models