Social Imitation Dynamics of Vaccination Driven by Vaccine Effectiveness and Beliefs

The invention of vaccine has significantly reduced the levels of morbidity and mortality from infectious diseases. However, the success of vaccines is often impaired by the free-rider problem: while vaccinated individuals incur the cost of vaccination, unvaccinated individuals are protected from the disease given that population immunity is in effect. This provides self-interested individuals an incentive to forgo vaccination. An emerging literature has investigated the epidemiology of individuals facing the free-rider problem given the choice of voluntary vaccination. Such studies properly apply the framework of game theory to describe how individuals react when facing the vaccination dilemma. In this paper, we extend previous work in imitation dynamics of vaccine uptake by accounting for imperfect vaccines, whose effects on individuals’ vaccination behavior on spatial populations have not been fully answered. We combine vaccination dynamics with an epidemiological model, in particular the SIR model. We then further extend our model to account for varying perceived vaccination costs during the decision-making for vaccination. The results from this paper show incomplete information together with ineffective vaccines in a population of imitators further aggravate the problem of suboptimal level of vaccination if the initial vaccination rate is low. A bi-stability phenomenon is observed: two separate equilibrium vaccination rates exist for high initial vaccination and low initial vaccination. When initial vaccination rate is high, vaccination rate moves to a high equilibrium. When initial vaccination rate is low, vaccination rate moves to a low equilibrium. The effect is observed when the population is homogeneous in terms of beliefs of vaccination effectiveness or heterogeneous with fixed beliefs or spreading beliefs. Our results provide support for intensifying vaccination campaigns to overcome vaccine hesitancy and to boost initial vaccination rate.