In this paper, we study the epidemic spreading in scale-free networks and propose a new susceptible-infected-recovered (SIR) model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Furthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.

h i g h l i g h t s• SIS epidemic dynamics is studied in metapopulation networks.• NIR and PIR heterogeneous infection regimes are proposed. • The two regimes both increase the threshold when only infected individuals move.• NIR increases and PIR decreases the threshold if two types of individuals both move.• We also explore the impact of the two regimes on the temporal behavior of epidemic. a b s t r a c tIn this paper, we study epidemic spreading in metapopulation networks wherein each node represents a subpopulation symbolizing a city or an urban area and links connecting nodes correspond to the human traveling routes among cities. Differently from previous studies, we introduce a heterogeneous infection rate to characterize the effect of nodes' local properties, such as population density, individual health habits, and social conditions, on epidemic infectivity. By means of a mean-field approach and Monte Carlo simulations, we explore how the heterogeneity of the infection rate affects the epidemic dynamics, and find that large fluctuations of the infection rate have a profound impact on the epidemic threshold as well as the temporal behavior of the prevalence above the epidemic threshold. This work can refine our understanding of epidemic spreading in metapopulation networks with the effect of nodes' local properties.

h i g h l i g h t s• We propose a time-varying human mobility pattern. • The pattern does not alter the epidemic threshold.• The pattern can lower the final density of infected individuals as a whole.• We derive a critical node degree leading to the presence of a transition. a b s t r a c tIn this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree k c . For nodes with degree smaller than k c , the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than k c , the pattern produces a negative impact on epidemic mitigation.