Global dynamics of a mathematical model for the possible re-emergence of polio

Motivated by studies warning about a possible re-emergence of poliomyelitis in Europe, we analyse a compartmental model for the transmission of polio describing the possible effect of unvaccinated people arriving to a region with low vaccination coverage. We calculate the basic reproduction number, and determine the global dynamics of the system: we show that, depending on the parameters, one of the two equilibria is globally asymptotically stable. The main tools applied are Lyapunov functions and persistence theory. We illustrate the analytic results by numerical examples, which also suggest that in order to avoid the risk of polio re-emergence, vaccinating the immigrant population might result insufficient, and also the vaccination coverage of countries with low rates should be increased.