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Open AccessArticle

Optimization of the Controls against the Spread of Zika Virus in Populations

1
Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA
2
Grupo Matemática Multidisciplinar, Facultad de Ingeniería, Universidad de los Andes, 5101 Mérida, Venezuela
3
Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 14071, Colombia
*
Author to whom correspondence should be addressed.
Computation 2020, 8(3), 76; https://doi.org/10.3390/computation8030076
Received: 16 July 2020 / Revised: 20 August 2020 / Accepted: 24 August 2020 / Published: 27 August 2020
(This article belongs to the Section Computational Biology)
In this paper, we study and explore two control strategies to decrease the spread of Zika virus in the human and mosquito populations. The control strategies that we consider in this study are awareness and spraying campaigns. We solve several optimal control problems relying on a mathematical epidemic model of Zika that considers both human and mosquito populations. The first control strategy is broad and includes using information campaigns, encouraging people to use bednetting, wear long-sleeve shirts, or similar protection actions. The second control is more specific and relies on spraying insecticides. The control system relies on a Zika mathematical model with control functions. To develop the optimal control problem, we use Pontryagins’ maximum principle, which is numerically solved as a boundary value problem. For the mathematical model of the Zika epidemic, we use parameter values extracted from real data from an outbreak in Colombia. We study the effect of the costs related to the controls and infected populations. These costs are important in real life since they can change the outcomes and recommendations for health authorities dramatically. Finally, we explore different options regarding which control measures are more cost-efficient for society. View Full-Text
Keywords: Zika virus; optimal control dynamical systems; Pontryagins’ maximum principle; epidemiological models Zika virus; optimal control dynamical systems; Pontryagins’ maximum principle; epidemiological models
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MDPI and ACS Style

González-Parra, G.; Díaz-Rodríguez, M.; Arenas, A.J. Optimization of the Controls against the Spread of Zika Virus in Populations. Computation 2020, 8, 76.

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