Adaptive dynamics for individual payoff game-theoretic models of vaccination

TL;DR

This paper models vaccination decisions using adaptive game dynamics, analyzing equilibrium stability and bifurcations to understand individual and collective health outcomes.

Contribution

It introduces an adaptive dynamics framework for vaccination game models, providing analytical insights into equilibrium stability and bifurcation behavior.

Findings

Existence of Nash equilibrium in vaccination game

Stability and bifurcation analysis of strategies

Analytical results supported by concrete examples

Abstract

Vaccination is widely recognised as one of the most effective forms of public health interventions. Individuals decisions regarding vaccination creates a complex social dilemma between individual and collective interests, where each person's decision affects the overall public health outcome. In this paper, we study the adaptive dynamics for the evolutionary dynamics of strategies in a fundamental game-theoretic model of vaticination. We show the existence of an (Nash) equilibrium and analyse the stability and bifurcations when varying the relevant parameters. We also demonstrate our analytical results by several concrete examples.