TY - GEN
T1 - SIRS dynamics on random networks: simulations and analytical models
AU - Rozhnova, Ganna
AU - Nunes, Ana
PY - 2009/12/1
Y1 - 2009/12/1
N2 - 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.
AB - 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.
KW - Oscillations
KW - Pair approximations
KW - Random regular graphs
KW - Stochastic epidemic models
UR - http://www.scopus.com/inward/record.url?scp=73649135248&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02466-5_78
DO - 10.1007/978-3-642-02466-5_78
M3 - Conference contribution
AN - SCOPUS:73649135248
SN - 3642024653
SN - 9783642024658
T3 - Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering
SP - 792
EP - 797
BT - Complex Sciences - First International Conference, Complex 2009, Revised Papers
T2 - 1st International Conference on Complex Sciences: Theory and Applications, Complex 2009
Y2 - 23 February 2009 through 25 February 2009
ER -