Abstract
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.
2 More- Received 20 February 2014
DOI:https://doi.org/10.1103/PhysRevX.4.041005
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Popular Summary
The description of the evolution of a single disease has been the recent subject of intense research given the outbreak of SARS that crippled the Asian continent in the early 2000s. However, in many situations, multiple pathogens coexist within the same host population and typically interact among each other, as in systems of competing pathogens (e.g., seasonal influenza) and diseases in which pathogens enhance or impair the spreading of other pathogens (e.g., HIV and tuberculosis). We develop a theoretical and computational framework to study the dynamics of two concurrent diseases and propose a model for the description of the simultaneous spreading of two interacting pathogens on the same host population through independent contact networks.
Our model is based on a heterogeneous mean-field approach for describing the critical properties of the dynamics of the disease. Furthermore, our numerical and analytical approach relies on an adequate framework for a temporal description of coupled-out-of-equilibrium outbreaks for two scenarios: the susceptible-infected-susceptible scenario and the susceptible-infected-removed scenario; the latter scenario assumes that an infected individual is removed from the system (via death, quarantine, etc.). With our proposed framework, we analytically derive the epidemic thresholds of the diseases modeled, and we explicitly address the influence on each threshold of factors such as the prevalence of the conjugate disease, the system size, the architecture of the networks of contacts, and the appearance of eventual correlations between the contacts. We additionally model the contagion and recovery processes and identify regions of parameter space where the two diseases can coexist. We find that the thresholds for an epidemic differ for the susceptible-infected-susceptible and susceptible-infected-removed scenarios; these thresholds can furthermore be time dependent.
Our findings provide deep insights into the key mechanisms that drive the evolution of interacting diseases. Our work additionally paves the way for the development of quantitative, data-driven models for a detailed characterization of concurrent and interacting diseases with the ultimate goal of forecasting epidemic outbreaks.