Persistence and dynamics in a metapopulation model of infection

We consider a metapopulation model of an Infectious Salmon Anemia virus (ISAv) infection on a network of patches connected via diffusion of the virus.  In addition  to previous results, we give analytical proof of oscillatory solutions in a system of 2 patches. We introduce a variety of network structures on n patches and show that, for all network structures under consideration, the basic reproduction number R0 can be determined via the next generation matrix approach.  We further show that R0>1 is the threshold for the persistence of the virus.