Spreading Behaviors on the Power-Law Growth Networks

This paper discusses the dynamics of the epidemic spreading behaviors for susceptible-infected-recovery (SIR) model on the power-law growth networks, characterized by variable value for exponent 7. We give the general generated algorithm for power-law growth networks, analyze the dynamics behavior for SIR model in complex networks, and introduce the interaction Markov chains mean-field equations as well as the stochastic numerical approach to examine the threshold (steady state) and time-independent behavior for the epidemic model on such network. We have done the simulation both for the BA networks and power-law growth networks. Analytical methods and simulated experiments show there exhibits a critical threshold for the pow-law growth networks below which it cannot diffuse in such type of the system. Meanwhile, results shows the stochastic numerical approach (SNA) can save memory and get the fast exploration, compared to the Monte Carlo calculations.