Svoboda | Graniru | BBC Russia | Golosameriki | Facebook
  • Open Access

Dynamics of Interacting Diseases

Joaquín Sanz, Cheng-Yi Xia, Sandro Meloni, and Yamir Moreno
Phys. Rev. X 4, 041005 – Published 8 October 2014

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
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

Authors & Affiliations

Joaquín Sanz1,2, Cheng-Yi Xia1,3, Sandro Meloni1, and Yamir Moreno1,2,4

  • 1Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50018, Spain
  • 2Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain
  • 3Key Laboratory of Computer Vision and System (Ministry of Education) and Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300191, People’s Republic of China
  • 4Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin 10126, Italy

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.

Key Image

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 4, Iss. 4 — October - December 2014

Subject Areas
Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×