A Game-Theoretic Model of Voluntary Yellow Fever Vaccination to Prevent Urban Outbreaks

Abstract

Yellow fever is a vector-borne acute viral hemorrhagic disease. It is endemic in tropical areas of Africa and Latin America but demonstrated the potential for international spread during the 2016 outbreak in Luanda, Angola. Yellow fever can be prevented by vaccination, vector control, and avoiding mosquito bites. To account for human behavior in disease dynamics, we add a game-theoretic component to a recent compartmental model of yellow fever transmission. The self-interested individuals evaluate the risks of contracting yellow fever and choose to vaccinate or avoid the bites to minimize the overall costs. We find the Nash equilibria, the optimal levels of vaccination and bite protections if the individuals can decide on the use of only one of the prevention methods as well as when they can decide on the use of both of them. In the later case, we show that vaccination is the preferred method of protection from the individual standpoint and, in the Nash equilibrium, individuals use vaccination only. Our model predicts the vaccination coverage in Angola to be around 65%, which is in reasonable agreement with the empirical value of 68%. We also study whether voluntary prevention can lead to the elimination of the disease in endemic areas. We show that voluntary vaccination alone is not enough to mitigate the risks of outbreaks, suggesting that a mandatory vaccination policy is necessary.

Keywords

• game theory
• vaccination games
• Nash equilibria
• yellow fever