Dynamics of Interacting Diseases

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level (be it a single population, a metapopulation system, or a network of contacts). In particular, interdependent contagion phenomena can be addressed only if we go beyond the scheme-one pathogen-one network. In this paper, we propose a framework that allows us to describe the spreading dynamics of two concurrent diseases. Specifically, we characterize analytically the epidemic thresholds of the two diseases for different scenarios and compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease's outbreak is conditioned to the prevalence levels of the other disease. Moreover, we show, for the susceptible-infected-susceptible scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the limit for scale-free networks. For the susceptible-infected-removed scenario, the phenomenology is richer and additional interdependencies show up. We also find that the secondary thresholds for the susceptible-infected-susceptible and susceptible-infected-removed models are different, which results directly from the interaction between both diseases. Our work thus solves an important problem and paves the way toward a more comprehensive description of the dynamics of interacting diseases.