Eur. Phys. J. B 65, 353-359 (2008)
https://doi.org/10.1140/epjb/e2008-00291-9

Infection fronts in contact disease spread

¹ Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany
² Department of Theoretical Physics, Kursk State University, 305000, Radishcheva 33, Kursk, Russia

Corresponding author: ^a igor.sokolov@physik.hu-berlin.de

Received: 8 January 2008
Revised: 22 May 2008
Published online: 18 July 2008

Abstract

We analyze the epidemic spread via a contact infection process in an immobile population within the Susceptible-Infected-Removed (SIR) model. We present both the results of stochastic simulations assuming different numbers of individuals (degrees of freedom) per cell as well as the solution of the corresponding deterministic equations. For the last ones we show that the appropriate system of nonlinear partial differential equations (PDE) allows for a complete separation of variables and present the approximate analytical expressions for the infection wave in different ranges of parameters. Comparing these results with the direct Monte-Carlo simulations we discuss the domain of applicability of the PDE models and their restrictions.