TITLE:
Optimal Control of a Vaccinating Game toward Increasing Overall Coverage
AUTHORS:
Monica G. Cojocaru, Ahmed S. Jaber
KEYWORDS:
Asymmetric Vaccination Game, Replicator Dynamics, Nash-Pareto Pair, Optimal Control
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.4,
April
24,
2018
ABSTRACT: 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.