Vaccination is a powerful public health tool (Fine et al., 2011). Still, individual choices to vaccinate often depend on the level of protection they believe others are providing. It directly links empirical measles trends to a game-theoretic tipping point for vaccination. The analysis began by examining global measles data to understand how vaccination rates impact disease cases (Ritchie, Roser, & Ortiz-Ospina, n.d.). A logistic regression model captured this relationship, showing a sharp decline in cases as coverage increased. This curve was then transformed into a benefit function (normalized between 0 and 1), which quantifies the level of indirect protection an individual receives based on how many others are vaccinated. Using this benefit function, individual decision making was modeled as a public goods game (Chaudhuri, 2011). Utility functions were derived for both strategies, and simulations were run to find the tipping point: the point where the expected benefit of free riding equals that of vaccinating (Bauch & Earn, 2004; Betsch et al., 2013).

It was found that when about 82.0 percent of the population is vaccinated, individuals become indifferent between the two choices at a cost of disease (d) of 10. To test the robustness of this result, sensitivity tests were conducted by varying the perceived cost of disease (d), using values of 5, 10, 15, and 20. Higher values of d shifted the tipping point to the right. Lower values of d had the opposite effect, making people stop vaccinating at lower coverage levels. Policymakers can use this model to guide strategies that reduce free riding and promote public health.