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Modelling and Optimal Control of Ebola Virus Disease in the Presence of Treatment and Quarantine of Infectives
International Journal of Systems Science and Applied Mathematics
Volume 5, Issue 4, December 2020, Pages: 43-53
Received: Oct. 30, 2020; Accepted: Nov. 11, 2020; Published: Nov. 23, 2020
Authors
Herick Laiton Kayange, Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania
Estomih Shedrack Massawe, College of Engineering and Technology, St. Joseph University in Tanzania, Dar es Salaam, Tanzania
Daniel Oluwole Makinde, Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa
Lathika Sunil Immanuel, College of Engineering and Technology, St. Joseph University in Tanzania, Dar es Salaam, Tanzania
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Abstract
In this paper, a non-linear mathematical model for the dynamics of Ebola virus diseases is formulated and analysed. The model has five classes namely susceptible human, exposed human, infected human, treated human and recovered human. Invariant region and positivity solution of the model are determined. Local stability analyses of disease free Equilibrium and endemic equilibrium are examined. The disease free equilibrium analysis is determined using Routh-Hurwitz criteria, whereby it is found to be locally stable if the reproduction number is less than one. Two control measures: control measure due to quarantine of exposed and susceptible individuals and control measure due to efficacy of treatment drug, used for treating Ebola virus disease Ebola victim are incorporated to the Ebola virus disease model. The control problem is then analysed in order to determine the optimal control. Numerical simulations for the model in the presence of control measures are finally performed. The results show that in the presence of optimal control, the Ebola virus disease can be eliminated in the Society. Furthermore, to minimize infections of Ebola virus disease, quarantine centres with skilled manpower must be prepared in advance so as to accommodate the significant number of exposed and susceptible individuals, in order to avoid further transmission in other areas out of quarantine centres. Also tracing of exposed and infected individuals must be efficiently done in order to quarantine the affected population and educate people on the transmission of the disease, symptoms and prevention measures in order to minimize human to human transmissions. Investing more on researches on new drugs which are effective in treating the Ebola virus disease victim is inevitable.
Keywords
Ebola, Control, Quarantine, Treatment, Infectives
Herick Laiton Kayange, Estomih Shedrack Massawe, Daniel Oluwole Makinde, Lathika Sunil Immanuel, Modelling and Optimal Control of Ebola Virus Disease in the Presence of Treatment and Quarantine of Infectives, International Journal of Systems Science and Applied Mathematics. Vol. 5, No. 4, 2020, pp. 43-53. doi: 10.11648/j.ijssam.20200504.12
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