Slovakia is one of the few European countries, where mandatory vaccination is enacted by law. However, recent frequent mass media discussions of the adverse effects of vaccination have gradually decreased compliance of parents: a shift from mandatory scheme to voluntary has become an issue to response.In this paper we estimate the epidemiological situation after an abolition of compulsory vaccination. We introduce two approaches howto formally describe incentive to vaccinate. In the first approach an equilibrium vaccination coverage is determined by a game theory concept,while in the second one the resulting equilibrium coverage is determined as the steady-state solution of a system of the differential equations.Both approaches are motivated by results of Bauch (2004, 2005). We make a synthesis of both approaches and discuss the results in the context of Slovakia.