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

doi:10.3934/mbe.2011.8.183

Mathematical Biosciences and Engineering

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

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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: 01 June 2010 Accepted: 29 June 2018 Published: 01 January 2011
MSC : Primary: 92B05, 49K21, 93C55; Secondary: 92D40.

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.
- antiviral treatment.,
- Influenza,
- optimal control,
- social distancing
Citation: Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics[J]. Mathematical Biosciences and Engineering, 2011, 8(1): 183-197. doi: 10.3934/mbe.2011.8.183

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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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