Newly emerging infectious diseases are expected to appear ever more frequently. Given the many uncertainties surrounding a new disease, we study global eradication efforts as a game of incomplete information. While models of disease eradication under perfect information tend to have multiple equilibria, we show that, for a world consisting of N ≥ 2 countries, even a small amount of uncertainty leads to equilibrium uniqueness. Our equilibrium has several implications. First, pandemics can be rational. Second, a rational pandemic may be inefficient. Third, less harmful diseases may cause more deaths. Our framework sheds light on the current COVID-19 pandemic.