Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks

Abstract

We investigate a fermionic susceptible-infected-susceptible model with the mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions P(k)∼k−γP(k)∼k−γ of exponents 2<γ<32<γ<3. Two diffusive processes with diffusion rate DD of an infected vertex are considered. In the standard diffusion, one of the nearest-neighbors is chosen with equal chance, while in the biased diffusion, this choice happens with probability proportional to the neighbor’s degree. A non-monotonic dependence of the epidemic threshold on DD with an optimum diffusion rate D∗D∗, for which the epidemic spreading is more efficient, is found for standard diffusion while monotonic decays are observed in the biased case. The epidemic thresholds go to zero as the network size is increased and the form that this happens depends on the diffusion rule and the degree exponent. We analytically investigated the dynamics using quenched and heterogeneous mean-field theories. The former presents, in general, a better performance for standard and the latter for biased diffusion models, indicating different activation mechanisms of the epidemic phases that are rationalized in terms of hubs or max kk-core subgraphs. Nowadays, we live in an interwoven world where information, goods, and people move through a complex structure with widely diversified types of interactions such as on-line friendship and airport connections. These and many other systems of completely distinct nature can be equally suited in a theoretical representation called complex networks, in which the elements are represented by vertices and the interactions among them by edges connecting these vertices. The study of epidemic processes on complex networks represents one of the cornerstones in modern network science and can aid the prevention (or even stimulation) of disease or misinformation spreading. The relevance of the interplay between diffusion and epidemic spreading in real systems is self-evident since hosts of infectious agents, such as people and mobile devices, are constantly moving, being the carriers that promote the quick transition from a localized outbreak to a large scale epidemic scenario. In this work, we perform a theoretical analysis and report nontrivial roles played by mobility of infected agents on the efficiency of epidemic spreading running on the top of complex networks. We expect that our results will render impacts for forthcoming research related to the area.