 Solution

The term $-IS$ removes healthy foxes through mass-action contact with infectives. The Laplacian ${\nabla }^{2}I$ models random migration of infected foxes. The matching term $+IS$ creates newly infected animals, while $-\mu I$ removes infectives at per-capita rate $\mu$. The equation $R_t=\mu I$ records those removed from infectious circulation, for example foxes that have died from rabies; they neither migrate nor return to susceptibility in this model.