Epidemic spreading on heterogeneous networks with identical infectivity

Abstract

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 meanfield 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.

A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency

“…Based on mean field theory [44][45][46][47] and the abovementioned hypothesis, the differential equations of the network diffusion model of food safety scare behavior under the effect of information transparency are…”

Strong ties promote the epidemic prevalence in susceptible–infected–susceptible spreading dynamics

“…If b = 0, the infected node randomly selects a neighbor to contact, equivalent to an unweighted SIS model [43]. If b > 0, strong ties are favored to constitute the paths of spreading, while if b < 0, weak ties are favored.…”

“…In sexual contact networks, although a few individuals have hundreds of sexual partners, their sexual activities are not far beyond a normal level due to the physiological limitations [41,42]. Therefore, in the present model we assume every individual has the same infectivity [39,43]. Without the lose of generality, at each time step, each infected node will select one of its neighbors to contact.…”

Global and partitioned reconstructions of undirected complex networks

“…Much evidence, from evolutionary games [2], gene regulatory networks [3], epidemic spreading and information diffusions [4], transportation and communication processes [5], etc., indicates that the topological structure of networks plays an important role in the dynamical behavior of networks. In addition, the network structure is also a basis for understanding and controlling complex networked systems [6,7,8].…”