Nick and Chris look into how math and game theory can predict vaccination uptake - the problem might be more complicated than you think. 

Googliography:

How Game Theory Could Solve the COVID-19 Rollout https://www.rand.org/blog/2021/03/how-game-theory-could-solve-the-covid-19-vaccine-rollout.html#:~:text=In%20past%20research%2C%20game%20theory,sent%20to%20each%20vaccination%20center

The Pandemic is a Prisoner's Dilemma (New York Times, Subscription Required) https://www.nytimes.com/2020/12/20/health/virus-vaccine-game-theory.html

The Vaccination Game: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC516577/

Social Distancing Game: https://royalsocietypublishing.org/doi/full/10.1098/rspa.2020.0686