Evolutionary Game Theory and the Spread of Influenza

Abstract

Vaccination has been used to control the spread of infectious diseases for centuries with widespread success. Deterministic models studying the spread of infectious disease often use the assumption of mass vaccination; however, these models do not allow for the inclusion of human behaviour. Since current vaccination campaigns are voluntary in nature, it is important to extend the study of infectious disease models to include the effects of human behaviour. To model the effects of vaccination behaviour on the spread of influenza, we examine a series of models in which individuals vaccinate according to memory or individual decision-making processes based upon self-interest. Allowing individuals to vaccinate proportionally to an exponentially decaying memory function of disease prevalence, we demonstrate the existence of a Hopf bifurcation for short memory spans. Using a game-theoretic influenza model, we determine that lowering the perceived vaccine risk may be insufficient to increase coverage to established target levels. Utilizing evolutionary game theory, we examine models with imitation dynamics both with and without a decaying memory function and show that, under certain conditions, periodic dynamics occur without seasonal forcing. Our results suggest that maintaining diseases at low prevalence with voluntary vaccination campaigns could lead to subsequent epidemics following the free-rider dilemma and that future research in disease control reliant on individual-based decision-making need to include the effects of human behaviour.