Vaccination Decisions in Triadic Interactions: A Coupled ODE Approach

This paper presents a mathematical model of vaccination decision-making in small social groups using triadic game theory. It employs coupled ordinary differential equations to illustrate the evolution of vaccination intensities among three individuals, influenced by interaction coefficients that reflect their interconnected decisions. The analysis explores scenarios in which one individual’s vaccination stance remains fixed. When the first individual maintains a constant stance, the system exhibits exponential growth or decay. Conversely, if the second individual is fixed, the system displays oscillatory behavior with declining vaccination rates. Additionally, the model is extended to include two coupled triads involving five individuals, revealing emergent behaviors that are not present in isolated groups. The findings emphasize differences in group stability based on which member serves as the decision anchor. This research establishes a mathematical foundation for understanding collective behavior in small social clusters and suggests potential avenues for future studies on vaccination decision-making in families, friend groups, and workplaces.