Mean Field Approximation to a Spatial Host-Pathogen Model

TL;DR

This paper refines the mean field approximation for a spatial host-pathogen model, correcting previous low-density assumptions and deriving more accurate equations including pair-correlations, with implications for understanding pathogen invasion.

Contribution

It provides the correct mean field equations and pair-correlation equations for the model, improving upon previous low-density approximations.

Findings

Corrected mean field equations for the model

Derived equations including pair-correlations

Discussed pathogen invasion dynamics

Abstract

We study the mean field approximation to a simple spatial host-pathogen model that has been shown to display interesting evolutionary properties. We show that previous derivations of the mean field equations for this model are actually only low-density approximations to the true mean field limit. We derive the correct equations and the corresponding equations including pair-correlations. The process of invasion by a mutant type of pathogen is also discussed. [This article was published as Physical Review E 67, 047102 (2003). Errata for the published version are corrected here and explicitly listed at the end of this document.]