Epidemic spreading with nonlinear infectivity in weighted scale-free networks

Abstract

Abstract. In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent α and the weight exponent β into the analytical SIR model, then examine the combination effects of α and β on the epidemic threshold and phase transition. We show that one can adjust the values of α and β to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence R grows in an exponential form in the early stage, then follows hierarchical dynamics. Furthermore, we find α is more sensitive than β in the transformation of the epidemic threshold and epidemic prevalence, which might deliver some useful information or new insights in the epidemic spreading and the correlative immunization schemes.

Epidemic spreading in weighted networks: An edge-based mean-field solution

“…Chu et al [25] investigated the same dynamical process upon weighted scale-free networks with community structure, and they showed that the weights of edges among different communities have higher impacts than those of edges inside communities. Chu et al [26] further studied the susceptible-infected-recovered (SIR) model and found that the weight distribution has a considerable impact on both epidemic threshold and prevalence. Karsai et al [27] considered the contact process in weighted scale-free * zhutou@ustc.edu networks, in which the weight of an edge connecting two higher-degree nodes is relatively small.…”

An ACP Approach to Public Health Emergency Management: Using a Campus Outbreak of H1N1 Influenza as a Case Study

“…This of course, limits the model's capability of providing a realistic description of how agents contact each other. Epidemic spread dynamics in weighted networks has begun to be studied through network-based models in recent years [29]- [32], and information on the contact frequency was usually obtained from survey [33]- [36].…”

“…In addition, while an agent's contact pattern with others largely depends on its geographic and network locations, it also varies with the frequency in which an agent contacts others. The diffusion speed of epidemics thus not only depends on the topological structure of networks (i.e., scale free or small world) [28]- [32], [37]- [41], but also depends on the strength of links among agents. We found very few studies used a weighted social network in agent-based epidemiological models.…”

Traffic-driven SIR epidemic spreading in networks

“…Due to the complexity of real-world networks, the mean-field approach [6][7][8] and the generating function approach [9] are used to drive the analytic results of epidemics spreading. Also, effects of degree correlations [15], clustering [16,17], weights and directions of edges [7,18,19] on epidemic spreading are broadly discussed. For SIR model, it was found that in the thermodynamic limit, not only the threshold tends to vanish, but also the time for the stabilization of the infection becomes very small [10,11].…”