Eur. Phys. J. B 67, 377-383 (2009)
https://doi.org/10.1140/epjb/e2008-00435-y

SIR model of epidemic spread with accumulated exposure

¹ M. Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30–, 059 Kraków, Poland
² Center for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark

Corresponding author: ^a bartek@th.if.uj.edu.pl

Received: 27 December 2007
Revised: 27 October 2008
Published online: 4 December 2008

Abstract

We study an extended and modified SIR model of epidemic spread in which susceptible agents during interactions with infectious neighbors are exposed to the disease and can consequently become infectious. The studied model is extended to include heterogeneity of interactions which is modelled assuming random character of the dose accumulated by susceptible agents in every interaction with infectious neighbors. When the accumulated exposure is larger than the individual's resistance, an agent becomes infectious and consequently introduces a new source of an epidemic which is capable of passing the disease further. We study statistical properties characterizing the course of an epidemic. The examination of the modified SIR model reveals a possible `resonant activation'-like behavior of the system in the duration of the epidemic outbreak and a possible bistable behavior of the model with accumulated exposure. Furthermore, the linear scaling of the duration of the epidemic with the system size for a wide range of the model parameters is recorded.