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.

[1]  I. Longini,et al.  The critical vaccination fraction for heterogeneous epidemic models. , 2003, Mathematical biosciences.

[2]  O. Diekmann Mathematical Epidemiology of Infectious Diseases , 1996 .

[3]  Paul R. Milgrom,et al.  Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities , 1990 .

[4]  Sarang Deo,et al.  Cournot Competition Under Yield Uncertainty: The Case of the U.S. Influenza Vaccine Market , 2009, Manuf. Serv. Oper. Manag..

[5]  H. Carlsson,et al.  Global Games and Equilibrium Selection , 1993 .

[6]  F. Ball,et al.  Dynamic population epidemic models. , 1991, Mathematical biosciences.

[7]  C. Macken,et al.  Mitigation strategies for pandemic influenza in the United States. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Leslie M. Marx,et al.  Dynamic Voluntary Contribution to a Public Project , 2000 .

[9]  A. Nizam,et al.  Containing Pandemic Influenza at the Source , 2005, Science.

[10]  Ralph L. Keeney,et al.  Repeated Commit-or-Defer Decisions with a Deadline: The Influenza Vaccine Composition , 2008, Oper. Res..

[11]  D. Cummings,et al.  Strategies for containing an emerging influenza pandemic in Southeast Asia , 2005, Nature.

[12]  Daryl J. Daley,et al.  Epidemic Modelling: An Introduction , 1999 .

[13]  Soo-Haeng Cho,et al.  The Optimal Composition of Influenza Vaccines Subject to Random Production Yields , 2010, Manuf. Serv. Oper. Manag..

[14]  D. M. Topkis Supermodularity and Complementarity , 1998 .

[15]  J. Huyck,et al.  Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure , 1990 .

[16]  Roger B. Myerson,et al.  Game theory - Analysis of Conflict , 1991 .

[17]  Margaret L. Brandeau,et al.  Allocating Resources to Control Infectious Diseases , 2005 .

[18]  Frank Ball,et al.  Stochastic multi-type SIR epidemics among a population partitioned into households , 2001, Advances in Applied Probability.

[19]  M. Brandeau,et al.  Resource allocation for control of infectious diseases in multiple independent populations: beyond cost-effectiveness analysis. , 2003, Journal of health economics.

[20]  Ray Higginson,et al.  The threat of an avian influenza pandemic. , 2005, British journal of nursing.

[21]  P. Ward,et al.  Oseltamivir (Tamiflu) and its potential for use in the event of an influenza pandemic. , 2005, The Journal of antimicrobial chemotherapy.

[22]  G. Grime,et al.  Distribution of dissolved iron in sediment pore waters at submillimetre resolution , 1991, Nature.

[23]  H. Varian,et al.  On the private provision of public goods , 1986 .

[24]  Richard C. Larson,et al.  Simple Models of Influenza Progression Within a Heterogeneous Population , 2007, Oper. Res..

[25]  J. Lau,et al.  Perceptions about status and modes of H5N1 transmission and associations with immediate behavioral responses in the Hong Kong general population. , 2006, Preventive medicine.

[26]  Alan S. Perelson,et al.  Optimization of Influenza Vaccine Selection , 2005, Oper. Res..

[27]  Huseyin Yildirim,et al.  Getting the Ball Rolling: Voluntary Contributions to a Large-Scale Public Project , 2006 .

[28]  J. Huyck,et al.  Strategic Uncertainty, Equilibrium Selection, and Coordination Failure in Average Opinion Games , 1991 .

[29]  Susan Mallett,et al.  A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals. , 2003, The Journal of antimicrobial chemotherapy.

[30]  Carl T. Bergstrom,et al.  Pandemic Influenza: Risk of Multiple Introductions and the Need to Prepare for Them , 2006, PLoS medicine.

[31]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[32]  D. Earn,et al.  Vaccination and the theory of games. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Stephen Morris,et al.  Equilibrium Selection in Global Games with Strategic Complementarities , 2001, J. Econ. Theory.

[34]  S. Baliga,et al.  Arms Races and Negotiations , 2002 .

[35]  David Simchi-Levi,et al.  Supply Chain Coordination and Influenza Vaccination , 2008, Oper. Res..

[36]  Diane Clemison Preparing for an influenza pandemic. , 2007, Community practitioner : the journal of the Community Practitioners' & Health Visitors' Association.

[37]  M Elizabeth Halloran,et al.  Design and evaluation of prophylactic interventions using infectious disease incidence data from close contact groups , 2006, Journal of the Royal Statistical Society. Series C, Applied statistics.