Research ArticleNo Access

Mathematical modeling of contact tracing as a control strategy of Ebola virus disease

Department of Science, Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Pretoria 0028, South Africa

Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon

E-mail Address: berge.tsanou@up.ac.za

E-mail Address: bergetsanou@yahoo.fr

Corresponding author.

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A. J. Ouemba Tassé

Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon

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H. M. Tenkam

Department of Mathematics and Applied Mathematics, North-West University, Private Bag X1290, Potchefstroom 2520, South Africa

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, and

J. Lubuma

Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67, Dschang, Cameroon

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https://doi.org/10.1142/S1793524518500936Cited by:23 (Source: Crossref)

Abstract

More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number $ℛ_{c}$ of each sub-model and for the full model are computed. Theoretically, we prove that when $ℛ_{c}$ is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when $ℛ_{c}$ is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.

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