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Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

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  • Amira Rachah
  • Delfim F. M. Torres

Abstract

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

Suggested Citation

  • Amira Rachah & Delfim F. M. Torres, 2015. "Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, May.
    • Handle: RePEc:hin:jnddns:842792
    DOI: 10.1155/2015/842792
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    Citations

    RePEc Biblio mentions

    As found on the RePEc Biblio, the curated bibliography for Economics:
    1. > Economics of Welfare > Health Economics > Economics of Pandemics > Specific pandemics > Ebola

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    Cited by:

    1. Ozyapici, Ali & Bilgehan, Bülent, 2018. "Generalized system of trial equation methods and their applications to biological systems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 722-732.
    2. Singh, Harendra, 2020. "Analysis for fractional dynamics of Ebola virus model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Ali Khaleel Dhaiban & Baydaa Khalaf Jabbar, 2021. "An optimal control model of COVID-19 pandemic: a comparative study of five countries," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 790-809, December.
    4. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    5. Doungmo Goufo, Emile F. & Kumar, Sunil & Mugisha, S.B., 2020. "Similarities in a fifth-order evolution equation with and with no singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. Dokuyucu, Mustafa Ali & Dutta, Hemen, 2020. "A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Boukhobza, Meriem & Debbouche, Amar & Shangerganesh, Lingeshwaran & Torres, Delfim F.M., 2024. "Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    8. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Vaishnav, Vaibhav & Vajpai, Jayashri, 2020. "Assessment of impact of relaxation in lockdown and forecast of preparation for combating COVID-19 pandemic in India using Group Method of Data Handling," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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