Encounter times in overlapping domains: application to epidemic spread in a population of territorial animals

TL;DR

This paper introduces an analytical approach to compute encounter times between territorial animals in one dimension, linking microscopic spatial behaviors to the macroscopic spread of epidemics.

Contribution

The study presents a novel analytical method for calculating encounter times in territorial populations and applies it to model epidemic spread dynamics.

Findings

Accurate analytical calculation of encounter times in territorial settings.

Derived epidemic propagation speed based on spatial and behavioral parameters.

Validated results with numerical simulations.

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.