Mathematical Biosciences and Engineering (MBE)

Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza

Pages: 141 - 170, Volume 8, Issue 1, January 2011      doi:10.3934/mbe.2011.8.141

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Olivia Prosper - Department of Mathematics, University of Florida, Gainesville, FL 32611, United States (email)
Omar Saucedo - Department of Mathematics, Texas A&M University, College Station, TX 77843, United States (email)
Doria Thompson - Department of Mathematics, Spelman College, Atlanta, GA 30314, United States (email)
Griselle Torres-Garcia - School of Human Evolution and Social Change, Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ 85287, United States (email)
Xiaohong Wang - School of Human Evolution and Social Change, Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ 85287, United States (email)
Carlos Castillo-Chavez - Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287, United States (email)

Abstract: The lessons learned from the 2009-2010 H1N1 influenza pandemic, as it moves out of the limelight, should not be under-estimated, particularly since the probability of novel influenza epidemics in the near future is not negligible and the potential consequences might be huge. Hence, as the world, particularly the industrialized world, responded to the potentially devastating effects of this novel A-H1N1 strain with substantial resources, reminders of the recurrent loss of life from a well established foe, seasonal influenza, could not be ignored. The uncertainties associated with the reported and expected levels of morbidity and mortality with this novel A-H1N1 live in a backdrop of $36,000$ deaths, over 200,000 hospitalizations, and millions of infections (20% of the population) attributed to seasonal influenza in the USA alone, each year. So, as the Northern Hemisphere braced for the possibility of a potentially "lethal" second wave of the novel A-H1N1 without a vaccine ready to mitigate its impact, questions of who should be vaccinated first if a vaccine became available, came to the forefront of the discussion. Uncertainty grew as we learned that the vaccine, once available, would be unevenly distributed around the world. Nations capable of acquiring large vaccine supplies soon became aware that those who could pay would have to compete for a limited vaccine stockpile. The challenges faced by nations dealing jointly with seasonal and novel A-H1N1 co-circulating strains under limited resources, that is, those with no access to novel A-H1N1 vaccine supplies, limited access to the seasonal influenza vaccine, and limited access to antivirals (like Tamiflu) are explored in this study. One- and two-strain models are introduced to mimic the influenza dynamics of a single and co-circulating strains, in the context of a single epidemic outbreak. Optimal control theory is used to identify and evaluate the "best" control policies. The controls account for the cost associated with social distancing and antiviral treatment policies. The optimal policies identified might have, if implemented, a substantial impact on the novel H1N1 and seasonal influenza co-circulating dynamics. Specifically, the implementation of antiviral treatment might reduce the number of influenza cases by up to 60% under a reasonable seasonal vaccination strategy, but only by up to 37% when the seasonal vaccine is not available. Optimal social distancing policies alone can be as effective as the combination of multiple policies, reducing the total number of influenza cases by more than 99% within a single outbreak, an unrealistic but theoretically possible outcome for isolated populations with limited resources.

Keywords:  Seasonal Influenza, Control Theory, Basic Reproductive Number.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: June 2010;      Accepted: September 2010;      Available Online: January 2011.