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Mathematical Biosciences and Engineering (MBE)
 

A note on the use of optimal control on a discrete time model of influenza dynamics

Pages: 183 - 197, Volume 8, Issue 1, January 2011      doi:10.3934/mbe.2011.8.183

 
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Paula A. González-Parra - Program in Computational Science, The University of Texas at El Paso, El Paso, TX 79968-0514, United States (email)
Sunmi Lee - Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, United States (email)
Leticia Velázquez - Program in Computational Science, Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968-0514, 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: A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagin's maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.

Keywords:  Influenza, optimal control, social distancing, antiviral treatment.
Mathematics Subject Classification:  Primary: 92B05, 49K21, 93C55; Secondary: 92D40.

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

 References