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

Paula A. González-Parra; Sunmi Lee; Leticia Velázquez; Carlos Castillo-Chavez

doi:10.3934/mbe.2011.8.183

Article Contents

2011, Volume 8, Issue 1: 183-197. Doi: 10.3934/mbe.2011.8.183 open access

This issue Previous Article A note on the use of influenza vaccination strategies when supply is limited Next Article Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics

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

1.
Program in Computational Science, The University of Texas at El Paso, El Paso, TX 79968-0514
2.
Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287
3.
Program in Computational Science, Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968-0514
4.
Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287

Received: June 2010

Revised: September 2010

Published: December 2010

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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.

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Mathematics Subject Classification: Primary: 92B05, 49K21, 93C55; Secondary: 92D40.

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