Extensions to more than one population

Following \citet{Xiao_2010}, we model movement between populations using a dispersal matrix ΔAE, where A is the weighted adjacency matrix containing elements Akl indicating the proportion of population k (row) moving to population l (column) per unit time and E is a diagonal matrix representing emigration, where each entry \(\mathrm{E}_{kk}=\sum_{k=1}^n\mathrm{A}_{kl}\) where n is the number of populations. Thus, the whole system can be depicted by a set of three equations per strain i per population k: