An optimal control model to design strategies for reducing the spread of the Ebola virus disease

Rama Seck; Diène Ngom; Benjamin Ivorra; Ángel M. Ramos; Rama Seck; Diène Ngom; Benjamin Ivorra; Ángel M. Ramos

doi:10.3934/mbe.2022082

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 1746-1774. doi: 10.3934/mbe.2022082

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An optimal control model to design strategies for reducing the spread of the Ebola virus disease

1.
Laboratory of Numerical Analysis and Computer Science, Applied Mathematics Section, Gaston Berger University, Saint-Louis, 209-IRD & UMMISCO-UGB, Senegal
2.
Mathematics and Applications Laboratory, Mathematics Department, Assane Seck University, Bp: 523, Ziguinchor, 209-IRD & UMMISCO-UGB, Senegal
3.
Interdisciplinary Mathematics Institute, Department of Applied Mathematics and Mathematical Analysis, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain

Academic Editor: Masaki Ogura

Received: 20 August 2021 Accepted: 22 November 2021 Published: 16 December 2021

In this work, we formulate an epidemiological model for studying the spread of Ebola virus disease in a considered territory. This model includes the effect of various control measures, such as: vaccination, education campaigns, early detection campaigns, increase of sanitary measures in hospital, quarantine of infected individuals and restriction of movement between geographical areas. Using optimal control theory, we determine an optimal control strategy which aims to reduce the number of infected individuals, according to some operative restrictions (e.g., economical, logistic, etc.). Furthermore, we study the existence and uniqueness of the optimal control. Finally, we illustrate the interest of the obtained results by considering numerical experiments based on real data.
- epidemiological modeling,
- optimal control,
- Ebola virus disease,
- deterministic models
Citation: Rama Seck, Diène Ngom, Benjamin Ivorra, Ángel M. Ramos. An optimal control model to design strategies for reducing the spread of the Ebola virus disease[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1746-1774. doi: 10.3934/mbe.2022082

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Abstract

In this work, we formulate an epidemiological model for studying the spread of Ebola virus disease in a considered territory. This model includes the effect of various control measures, such as: vaccination, education campaigns, early detection campaigns, increase of sanitary measures in hospital, quarantine of infected individuals and restriction of movement between geographical areas. Using optimal control theory, we determine an optimal control strategy which aims to reduce the number of infected individuals, according to some operative restrictions (e.g., economical, logistic, etc.). Furthermore, we study the existence and uniqueness of the optimal control. Finally, we illustrate the interest of the obtained results by considering numerical experiments based on real data.

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