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Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries—Validation and Application to the 2014–2015 Ebola Virus Disease Epidemic

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Abstract

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial–temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014–2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

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Acknowledgments

This work was carried out thanks to the financial support of the Spanish “Ministry of Economy and Competitiveness” under Project MTM2011-22658; the “Junta de Andalucía” and the European Regional Development Fund through Project P12-TIC301; and the research group MOMAT (Ref. 910480) supported by “Banco de Santander” and “Universidad Complutense de Madrid.”

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Authors and Affiliations

  1. MOMAT Research Group, IMI-Institute and Applied Mathematics Department, Universidad Complutense de Madrid, Plaza de Ciencias, 3, 28040, Madrid, Spain

    Benjamin Ivorra & Ángel M. Ramos

  2. Département de Mathématiques, UFR des Sciences et Technologies, Université Assane Seck de Ziguinchor, Ziguinchor, Senegal

    Diène Ngom

  3. Laboratoire d’Analyse Numérique et d’ Informatique, Université Gaston Berger de Saint Louis, Saint-Louis, Senegal

    Diène Ngom

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  1. Benjamin Ivorra
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  2. Diène Ngom
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  3. Ángel M. Ramos
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Correspondence to Benjamin Ivorra.

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Ivorra, B., Ngom, D. & Ramos, Á.M. Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries—Validation and Application to the 2014–2015 Ebola Virus Disease Epidemic. Bull Math Biol 77, 1668–1704 (2015). https://doi.org/10.1007/s11538-015-0100-x

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  • DOI: https://doi.org/10.1007/s11538-015-0100-x

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