Migrations, vaccinations and epidemic control

We consider three regions with different public health conditions. In the absence of migration among these regions, the first two have good health conditions and the disease free state is stable; for the third region, on the other hand, the only stable state is the endemic one. When migration is included in the model, we assume that the second region has a disease risk that makes its inhabitants prone to accept to be vaccinated, while the population in the first region tends to reject the vaccination, considered riskier that the disease. Therefore, the second region is a “buffer zone” between the two extremal regions. We study the basic reproductive ratio as a function of the vaccination in all regions and migration among them. This problem is studied numerically, showing explicit situations in which migration will have an overall positive effect in the disease dynamics, with and without vaccinations. We also find explicit formula in the limit of small (“closed borders”) and high migration (“open borders”). keywords: Epidemic models, Vaccination, Meta-population, SIR model