Physics – Physics and Society
Scientific paper
2006-09-17
Physics Letters A 364, 189-193 (2007)
Physics
Physics and Society
5 pages, 3 figures
Scientific paper
10.1016/j.physleta.2006.12.021
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic results. Furthermore, we study the time behavior of the epidemic propagation and find a hierarchical dynamics with three plateaus. Once the highly connected hubs are reached, the infection pervades almost the whole network in a progressive cascade across smaller degree classes. Then, after the previously infected hubs are recovered, the disease can only propagate to the class of smallest degree till the infected individuals are all recovered. The present results could be of practical importance in the setup of dynamic control strategies.
Bai Wen-Jie
Ren Jie
Shi Zhi-Wen
Wang Bing-Hong
Wang Wen-Xu
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