Selfish drug allocation for containing an international influenza pandemic at the onset

Recent epidemiologic studies have suggested that the prophylactic use of antiviral drugs could slow down the spread of an influenza epidemic. Because drug stockpiles are presently scattered in different countries, the outbreak of an epidemic gives rise to a game in which each country must make decisions about how best to allocate its own stockpile in order to protect its population. We develop a two-period multivariate Reed-Frost model to represent the spread of the epidemic within and across countries at its onset. We consider the first two periods only to mimic the exponential growth of an epidemic in its early stage, while keeping the model tractable. Preliminary numerical studies suggest that insights from the two-period model hold in general when considering the entire time horizon. Our model captures three critical sources of uncertainty: the number of initial infections, the spread of the disease, and drug efficacy. We show that for small probabilities of between-country infections, the underlying game is supermodular, Nash equilibrium exists, and there is a unique one that is Pareto optimal among all existing equilibria. Further, we identify sufficient conditions under which the optimal solution of a central planner (such as the World Health Organization) constitutes a Pareto improvement over the decentralized equilibrium, suggesting that countries should agree on an allocation scheme that would benefit everyone. By contrast, when the central planner's solution does not constitute a Pareto improvement, minimizing the total number of infected persons globally requires some countries to sacrifice part of their own population, which raises intriguing ethical issues.