Erik M. Rauch, Marcus A.M. de Aguiar, and Yaneer Bar-Yam, Mean field approximation to a spatial host-pathogen model, Physical Review E 67: 047102 (2003).
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.