Epidemic spreading through direct and indirect interactions.

In this paper we study the susceptible-infected-susceptible epidemic dynamics, considering a specialized setting where popular places (termed passive entities) are visited by agents (termed active entities). We consider two types of spreading dynamics: direct spreading, where the active entities infect each other while visiting the passive entities, and indirect spreading, where the passive entities act as carriers and the infection is spread via them. We investigate in particular the effect of selection strategy, i.e., the way passive entities are chosen, in the spread of epidemics. We introduce a mathematical framework to study the effect of an arbitrary selection strategy and derive formulas for prevalence, extinction probabilities, and epidemic thresholds for both indirect and direct spreading. We also obtain a very simple relationship between the extinction probability and the prevalence. We pay special attention to preferential selection and derive exact formulas. The analysis reveals that an increase in the diversity in the selection process lowers the epidemic thresholds. Comparing the direct and indirect spreading, we identify regions in the parameter space where the prevalence of the indirect spreading is higher than the direct one.