Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools
Applied and Computational Mathematics
Volume 8, Issue 2, April 2019, Pages: 29-36
Received: Mar. 12, 2019;
Accepted: Apr. 15, 2019;
Published: May 15, 2019
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Michael Uchenna, Department of Mathematics, Alex Ekwueme Federal University Ndufu Alike, Ikwo, Abakaliki, Nigeria
Offia Akachukwu, Department of Mathematics, Alex Ekwueme Federal University Ndufu Alike, Ikwo, Abakaliki, Nigeria
Elebute Kafayat, Department of Mathematics, Alex Ekwueme Federal University Ndufu Alike, Ikwo, Abakaliki, Nigeria
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Developing countries are prone to some outburst of epidemic because of the poor sanitary apparatus in existence in the public schools where more - likely those children from the underdogs will be seen. Conjunctivitis is one of such communicable disease in western sub – Sahara Africa because of the topography, level of education in the rural communities and the degree of poverty that rocks an average family. Model for transmission dynamics of acute conjunctivitis is proposed and analyzed both analytically and numerically. The model is reformulated as an optimal control problem taking into consideration the effect of proper sanitation and training of the educators; and Maximum Principle was employed to obtain the necessary conditions for existence of optimal control. The basic reproduction number is obtained using the next generation matrix and spectral radius which is less than one when computed. The result shows an agreement of the analytical and numerical solution; in addition, if the sanitation that includes the serenity of the school environment, conduciveness of the classrooms, personal hygiene are dually observed in and outside the school, and education of the caregivers which includes the teachers, menders, parents and even the pupils are articulated properly, the infected pupils shall be decreased drastically over time.
Conjunctivitis, Stability, Optimal Control, Mathematical Model
To cite this article
Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools, Applied and Computational Mathematics.
Vol. 8, No. 2,
2019, pp. 29-36.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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