Author(s)

Monica G. Cojocaru¹, Ahmed S. Jaber^1,2

¹Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada.
²Department of Mathematics, College of Science, University of Al-Mustansiriya, Baghdad, Iraq.

In this paper, we study an asymmetric game that characterizes the intentions of players to adopt a vaccine. The game describes a decision-making process of two players differentiated by income level and perceived treatment cost, who consider a vaccination against an infectious disease. The process is a noncooperative game since their vaccination decision has a direct impact on vaccine coverage in the population. We introduce a replicator dynamics (RD) to investigate the players’ optimal strategy selections over time. The dynamics reveal the long-term stability of the unique Nash-Pareto equilibrium strategy of this game, which is an extension of the notion of an evolutionarily stable strategy pair for asymmetric games. This Nash-Pareto pair is dependent on perceived costs to each player type, on perceived loss upon getting infected, and on the probability of getting infected from an infected person. Last but not least, we introduce a payoff parameter that plays the role of cost-incentive towards vaccination. We use an optimal control problem associated with the RD system to show that the Nash-Pareto pair can be controlled to evolve towards vaccination strategies that lead to a higher overall expected vaccine coverage.

Asymmetric Vaccination Game, Replicator Dynamics, Nash-Pareto Pair, Optimal Control

Cojocaru, M. and Jaber, A. (2018) Optimal Control of a Vaccinating Game toward Increasing Overall Coverage. Journal of Applied Mathematics and Physics, 6, 754-769. doi: 10.4236/jamp.2018.64067.