We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness. The interplay between awareness and epidemic dynamics in networks has recently achieved much attention. The human responses to disease outbreaks can result in the reduction of susceptibility to infection, which in turn, can affect epidemic dynamics. So an epidemic model should include such factors. This issue has been studied from the perspective of awareness reactions. However, the impact of individual awareness is not entirely understood thus far because of its variety and complexity. In this work, we build a continuous mean-field (MF) model to study the impact of the three forms of awareness on the epidemic spreading in a finite scale-free (SF) network: contact awareness that increases with individual contact number; local awareness that increases with the fraction of infected contacts; and global awareness that increases with the overall disease prevalence. Theoretical analysis and simulation shows that the effect of these different types of awareness can be clearly classified. Both the contact awareness and the local awareness can raise the epidemic threshold, while the global awareness can only decrease the epidemic prevalence. These results also tell us that individual awareness contributes toward the inhibition of epidemic transmission.

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Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infectedsusceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.

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By using the microscopic Markov-chain approximation approach, we investigate the epidemic spreading and the responsive immunization in social networks. It is assumed that individual vaccination behavior depends on the local information of an epidemic. Our results suggest that the responsive immunization has negligible impact on the epidemic threshold and the critical value of initial epidemic outbreak, but it can effectively inhibit the outbreak of epidemic. We also analyze the influence of the intervention on the disease dynamics, where the vaccination is available only to those individuals whose number of neighbors is greater than a certain value. Simulation analysis implies that the intervention strategy can effectively reduce the vaccine use under the epidemic control.

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