Dynamics of epidemics on random networks

M. Marder
Phys. Rev. E 75, 066103 – Published 13 June 2007

Abstract

This paper examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one that is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.

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  • Received 9 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.066103

©2007 American Physical Society

Authors & Affiliations

M. Marder*

  • Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA

  • *Electronic address: marder@mail.utexas.edu

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Issue

Vol. 75, Iss. 6 — June 2007

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