The infection dynamics of vertically transmitted viruses in a two-population model

There is a growing interest in vertically transmitted viruses. Field studies show that virus infection frequency often varies in space and time. In order to understand the spatial variation of virus prevalence, we designed a mathematical model describing the infection dynamics of a biparentally inherited virus in a two-population model. Model parameters are paternal and maternal transmission rates, cost of infection, and up to two migration rates. We investigated three different population structures: (1) a single panmictic host population, (2) two populations connected by uni-directional migration (mainland-island model), and (3) two populations connected by two-way migration. According to the results, the parameter space can be divided in three zones: (1) viral spread, (2) no viral spread, (3) bistability (in a single population) or stable infection polymorphism (in the two-population models). The finding of bistability is interesting and new. It shows that infected and uninfected populations can stably coexist, if migration is below a critical value, and if the cost of infection is moderately high. In summary, our results show that spatial structure of host populations is an important factor in determining geographical differences of vertically transmitted viruses.