On Evolutionary Vaccination Game in Activity-Driven Networks

Abstract

Since human face-to-face communications change over time, their perceived probabilities associated with uncertain outcomes usually present a nonlinear fashion in reality. This article incorporates both humans active characteristics and risk perception into epidemic spreading and explores a comprehensive evolutionary vaccination game in activity-driven networks. According to the weighting effect, the individuals’ activity rate thresholds are obtained in different cases under the framework of the pure Nash equilibrium. Furthermore, how the number of connected edges of activated individuals <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> and infection rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> affect individuals’ vaccination, decision-making is theoretically analyzed. It is proven that some unvaccinated individuals gradually become vaccinated individuals with the increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> . Moreover, there is a unique pure Nash equilibrium social state (Pareto optimization), and the pure Nash equilibrium together with Pareto optimization has the same equilibrium for our proposed evolutionary vaccination game, which provides an alternative condition judging the stability of game system. In the case of complete information and individual complete rationality, the factors, including vaccination cost, individuals’ activity rate, the number of connected edges of activated individuals, and infection rate, have a significant influence on the final average social cost.