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Stochastic dynamics for reinfection by transmitted diseases

Alessandro S. Barros and Suani T. R. Pinho
Phys. Rev. E 95, 062135 – Published 29 June 2017

Abstract

The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σβ than infection rate β). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ<1) and social contagions (σ>1).

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  • Received 8 February 2016
  • Revised 30 April 2017

DOI:https://doi.org/10.1103/PhysRevE.95.062135

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

Alessandro S. Barros*

  • Departamento de Física, Instituto Federal da Bahia-40110-150 Salvador, Brazil

Suani T. R. Pinho

  • Instituto de Física, Universidade Federal da Bahia-40210-340 Salvador, Brazil

  • *alessandrobarros@ifba.edu.br
  • suani@ufba.br

Article Text

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Issue

Vol. 95, Iss. 6 — June 2017

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