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

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.

arXiv comment5 pages, 4 figures

References in corpus (10)

• Forecast and Control of Epidemics in a Globalized World
• Geometry-controlled kinetics
• Invasion threshold in heterogeneous metapopulation networks
• Phase transitions in contagion processes mediated by recurrent mobility patterns
• Natural human mobility patterns and spatial spread of infectious diseases
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Extensions of Effective Medium Theory of Transport in Disordered Systems
• Exact encounter times for many random walkers on regular and complex networks
• How rare are diffusive rare events?
• Energy transport through rare collisions

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• Misconceptions about quantifying animal encounter and interaction processes
• Network Structures between Strategies in Iterated Prisoners' Dilemma Games
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• Drunken robber, tipsy cop: First passage times, mobile traps, and Hopf bifurcations
• Coupled effects of local movement and global interaction on contagion