Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study

Bruno Buonomo; Eleonora Messina

doi:10.3934/mbe.2012.9.539

Article Contents

2012, Volume 9, Issue 3: 539-552. Doi: 10.3934/mbe.2012.9.539

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Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study

Bruno Buonomo^1, and
Eleonora Messina^1,

1.
Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples

Received: March 31, 2011

Revised: February 29, 2012

Published: June 2012

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Abstract

When a newly emerging human infectious disease spreads through a host population, it may be that public health authorities must begin facing the outbreaks and planning an intervention campaign when not all intervention tools are readily available. In such cases, the problem of finding optimal intervention strategies to minimize both the disease burden and the intervention costs may be addressed by considering multiple intervention regimes. In this paper, we consider the scenario in which authorities may rely initially only on non-pharmaceutical interventions at the beginning of the campaign, knowing that a vaccine will later be available, at an exogenous and known switching time. We use a two-stage optimal control problem over a finite time horizon to analyze the optimal intervention strategies during the whole campaign, and to assess the effects of the new intervention tool on the preceding stage of the campaign. We obtain the optimality systems of two connected optimal control problems, and show the solution profiles through numerical simulations.

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Mathematics Subject Classification: Primary: 92D30, 49J15.

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