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Axioms 2018, 7(3), 61; https://doi.org/10.3390/axioms7030061

Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution

1
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
2
Centre of Excellence in Mathematics, Commission on Higher Education, Ministry of Education, 328 Sri Ayuthaya Road, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Received: 18 June 2018 / Revised: 17 August 2018 / Accepted: 18 August 2018 / Published: 23 August 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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Abstract

A dynamical model of Zika virus (ZIKV) epidemic with direct transmission, sexual transmission, and vertical transmission is developed. A sub-optimal control problem to counter against the disease is proposed including three controls: vector elimination, vector-to-human contact reduction, and sexual contact reduction. Each control variable is discretized into piece-wise constant intervals. The problem is solved by Differential Evolution (DE), which is one of the evolutionary algorithm developed for optimization. Two scenarios, namely four time horizons and eight time horizons, are compared and discussed. The simulations show that models with controls lead to decreasing the number of patients as well as epidemic period length. From the optimal solution, vector elimination is the prioritized strategy for disease control. View Full-Text
Keywords: Zika virus; sexual transmission; vertical transmission; sub-optimal control problem; differential evolution Zika virus; sexual transmission; vertical transmission; sub-optimal control problem; differential evolution
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chaikham, N.; Sawangtong, W. Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution. Axioms 2018, 7, 61.

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