Vaccination dilemma in the thermodynamic limit

Area of Science:

• Mathematical modeling of social behavior
• Epidemiology
• Game theory

Background:

• The vaccination game presents a social dilemma regarding individual immunization decisions during infectious disease outbreaks.
• Public perception of vaccines significantly influences disease dynamics, as highlighted by the COVID-19 pandemic.

Purpose of the Study:

• To analyze the vaccination game in the thermodynamic limit using Nash equilibrium (NE) mapping derived from the 1D Ising model.
• To compare NE mapping with Darwinian evolution (DE) and agent-based simulation (ABS) for predicting population vaccination behavior.

Main Methods:

• Analytical method using Nash equilibrium mapping derived from the 1D Ising model.
• Comparison with Darwinian evolution and agent-based simulation models.
• Application to the AstraZeneca vaccine risk-benefit analysis.

Main Results:

• Nash equilibrium mapping and agent-based simulation show agreement in predicting population vaccination behavior.
• Darwinian evolution models deviate significantly and inaccurately predict equilibrium behavior.
• Both NE mapping and ABS predict high AstraZeneca vaccine uptake (>40 years) but reveal reluctance in younger populations (20-39 years).

Conclusions:

• Nash equilibrium mapping is a reliable method for analyzing population-level vaccination decisions.
• Government interventions like mandates or campaigns may be necessary to encourage vaccination in younger demographics.
• Older populations demonstrate a strong propensity for vaccination, irrespective of perceived risks.