Mean-field theory of a recurrent epidemiological model

Viktor Nagy
Phys. Rev. E 79, 066105 – Published 9 June 2009

Abstract

Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.

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  • Received 6 February 2009

DOI:https://doi.org/10.1103/PhysRevE.79.066105

©2009 American Physical Society

Authors & Affiliations

Viktor Nagy

  • Department of Physics, Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 79, Iss. 6 — June 2009

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