Encounter Times in Overlapping Domains: Application to Epidemic Spread in a Population of Territorial Animals

Luca Giuggioli, Sebastian Pérez-Becker, and David P. Sanders
Phys. Rev. Lett. 110, 058103 – Published 30 January 2013

Abstract

We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding very good agreement with numerically exact calculations. We model a population of susceptible and infected territorial individuals with this spatial arrangement, and which may transmit an epidemic when they meet. We apply the results on encounter times to determine analytically the macroscopic propagation speed of the epidemic as a function of the microscopic characteristics: the confining geometry, the animal diffusion constant, and the infection transmission probability.

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  • Received 10 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.058103

© 2013 American Physical Society

Authors & Affiliations

Luca Giuggioli1,*, Sebastian Pérez-Becker2,†, and David P. Sanders2,‡

  • 1Bristol Centre for Complexity Sciences, Department of Engineering Mathematics and School of Biological Sciences, University of Bristol, BS8 1TR Bristol, United Kingdom
  • 2Departamento de Física, Facultad de Ciencias, and Centro de Ciencias de la Complejidad (C3), Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, Mexico

  • *luca.giuggioli@bristol.ac.uk
  • sebastian.perez.becker@gmail.com
  • dpsanders@ciencias.unam.mx

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Vol. 110, Iss. 5 — 1 February 2013

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