E. M. Rauch, M. A. M. de Aguiar, Y. Bar-Yam, Mean field approximation to a spatial host-pathogen model, Phys. Rev. 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.