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A pair of random walkers, the motion of each of which in two dimensions isconfined spatially by the action of a quadratic potential centered at differentlocations for the two walks, are analyzed in the context of reaction-diffusion.The application sought is to the process of transmission of infection inepidemics. The walkers are animals such as rodents in considerations of theHantavirus epidemic, infected or susceptible, the reaction is the transmissionof infection, and the confining potential represents the tendency of theanimals to stay in the neighborhood of their home range centers. Calculationsare based on a recently developed formalism (Kenkre and Sugaya, Bull. Math.Bio. 76, 3016 (2014)) structured around analytic solutions of a Smoluchowskiequation and one of its aims is the resolution of peculiar but well-knownproblems of reaction-diffusion theory in 2-dimensions. In the present analysis,reaction occurs not at points but in spatial regions of dimensions larger than0. The analysis uncovers interesting nonintuitive phenomena one of which issimilar to that encountered in the 1-dimensional analysis given in the quotedarticle, and another specific to the fact that the reaction region is spatiallyextended. The analysis additionally provides a realistic description ofobservations on animals transmitting infection while moving on what iseffectively a 2-dimensional landscape. Along with the general formalism andexplicit 1-dimensional analysis given in Bull. Math. Bio. 76, 3016 (2014), thepresent work forms a model calculational tool for the analysis for thetransmission of infection in dilute systems.

Confined Random Walkers in Dimensions Higher Than One and Analysis of Transmission of Infection in Epidemics