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Optimal Control of a Vaccinating Game toward Increasing Overall Coverage

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Document pages: 16 pages

Abstract: In this paper, we study an asymmetric game thatcharacterizes the intentions of players to adopt a vaccine. The game describesa decision-making process of two players differentiated by income level andperceived treatment cost, who consider a vaccination against an infectiousdisease. The process is a noncooperative game since their vaccination decisionhas a direct impact on vaccine coverage in the population. We introduce areplicator dynamics (RD) to investigate the players’ optimal strategyselections over time. The dynamics reveal the long-term stability of the uniqueNash-Pareto equilibrium strategy of this game, which is an extension of thenotion of an evolutionarily stable strategy pair for asymmetric games. ThisNash-Pareto pair is dependent on perceived costs to each player type, onperceived loss upon getting infected, and on the probability of gettinginfected from an infected person. Last but not least, weintroduce a payoff parameter that plays the role of cost-incentive towardsvaccination. We use an optimal control problem associated with the RD system toshow that the Nash-Pareto pair can be controlled to evolve towards vaccinationstrategies that lead to a higher overall expected vaccine coverage.

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