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Register a new userSynergistic epidemic spreading in correlated networks
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We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model, which accurately describe the synergistic SIS dynamics. We quantitatively confirm all qualitative predictions of the mean-field treatment in numerical evaluations of the approximate master equations.
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In spite of the extensive previous efforts on traffic dynamics and epidemic spreading in complex networks, the problem of traffic-driven epidemic spreading on {em correlated} networks has not been addressed. Interestingly, we find that the epidemic threshold, a fundamental quantity underlying the spreading dynamics, exhibits a non-monotonic behavior in that it can be minimized for some critical value of the assortativity coefficient, a parameter characterizing the network correlation. To understand this phenomenon, we use the degree-based mean-field theory to calculate the traffic-driven epidemic threshold for correlated networks. The theory predicts that the threshold is inversely proportional to the packet-generation rate and the largest eigenvalue of the betweenness matrix. We obtain consistency between theory and numerics. Our results may provide insights into the important problem of controlling/harnessing real-world epidemic spreading dynamics driven by traffic flows.
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Albeit epidemic models have evolved into powerful predictive tools for the spread of diseases and opinions, most assume memoryless agents and independent transmission channels. We develop an infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Analytic equations and simulations of the susceptible-infected-susceptible model in unstructured substrates reveal the emergence of an additional phase that separates the usual healthy and endemic ones. This intermediate phase shows fundamentally distinct characteristics, and the system exhibits either excitability or an exotic variant of bistability. Moreover, the transition to endemicity presents hybrid aspects. These features are the product of an intricate balance between two memory modes and indicate that non-Markovian effects significantly alter the properties of spreading processes.
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