SIRS epidemics on complex networks: Concurrence of exact Markov chain and approximated models

Abstract— We study the SIRS (Susceptible-InfectedRecovered-Susceptible) spreading processes over complex networks, by considering its exact 3n -state Markov chain model. The Markov chain model exhibits an interesting connection with its 2n-state nonlinear “mean-field” approximation and the latter’s corresponding linear approximation. We show that under the specific threshold where the disease-free state is a globally stable fixed point of both the linear and nonlinear models, the exact underlying Markov chain has an O(log n) mixing time, which means the epidemic dies out quickly. In fact, the epidemic eradication condition coincides for all the three models. Furthermore, when the threshold condition is violated, which indicates that the linear model is not stable, we show that there exists a unique second fixed point for the nonlinear model, which corresponds to the endemic state. We also investigate the effect of adding immunization to the SIRS epidemics by introducing two...

• Type: Journal
• Year: 2015
• Where: CDC
• Authors: Navid Azizan Ruhi, Babak Hassibi
• Keywords: CDC 2015, Control Systems