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Journal of Applied Sciences and Environmental Management
World Bank assisted National Agricultural Research Project (NARP) - University of Port Harcourt
ISSN: 1119-8362
Vol. 21, No. 4, 2017, pp. 663-671
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Bioline Code: ja17071
Full paper language: English
Document type: Research Article
Document available free of charge
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Journal of Applied Sciences and Environmental Management, Vol. 21, No. 4, 2017, pp. 663-671
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Stability Analysis of a Mathematical Model for Onchocerciaisis Disease Dynamics
BAKO, DU; AKINWANDE, NI; ENAGI, AI; KUTA, FA & ABDULRAHMAN, S
Abstract
In this work, we propose a Deterministic Mathematical Model that Combines
Infectious but not Blind and Infectious Blind Compartments for Onchocerciasis Transmission
and Control. Onchocerciasis is usually the term used to describe river blindness, it is a disease
that causes blindness, and the second largest cause of blindness after trachoma. It mainly affects
the eyes and the skin. The equilibrium states of the model are obtained. The disease free
equilibrium state is analysed for stability; the condition for its stability is obtained as an
inequality constraint on the parameters. Results shows that although, a 60% treatment coverage
rate of infected and infectious blind individuals only is better than 80% treatment coverage rate
of infected but not blind individuals only. Also, all the four control strategies reduce the
effective reproduction number below unity. A 40% coverage rate of fumigation and treatment of
infectious but not blind is better than a 40%coverage rate of fumigation only. It further reveals
that a 30% coverage rate of fumigation and treatment of infectious blind is better than
80%coverage rate of fumigation only or fumigation and treatment of infected but not blind only.
We are able to show that disease free equilibrium and endemic equilibrium exists and are both
locally and globally stable, and we computed the Rc of the model and showed that it is a
parameter to test for stability, we also use the Jacobi stability technique to show that disease free
equilibrium and endemic equilibrium are both locally and globally stable. The sensitivity
analysis results shows that the most sensitive parameter is ρ while the least sensitive is μv ,
Keywords
Onchocerciasis; Mathematical model; Equilibrium state; Deterministic; Effective reproductive number; Stability
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© Copyright 2017 - Journal of Applied Sciences and Environmental Management
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