Volume 8, Issue 2, April 2019, Page: 29-36
Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools
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
Received: Mar. 12, 2019;       Accepted: Apr. 15, 2019;       Published: May 15, 2019
DOI: 10.11648/j.acm.20190802.11      View  51      Downloads  22
Abstract
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.
Keywords
Conjunctivitis, Stability, Optimal Control, Mathematical Model
To cite this article
Michael Uchenna, Offia Akachukwu, Elebute Kafayat, Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools, Applied and Computational Mathematics. Vol. 8, No. 2, 2019, pp. 29-36. doi: 10.11648/j.acm.20190802.11
Copyright
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/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Murray J. D., Mathematical Biology I. (2003) Springer – Verlag Berlin Heidelbery.
[2]
Kyere S. N., Boateng F. A., Hoggar G. F., Jonathan P. (2018) Optimal Control Model of Haemorrhagic conjunctivitis disease. Adv. Comput. Sci, 1(2): 108.
[3]
The centers for disease control and prevention, March, 2018.
[4]
American Academy of pediatrics. Red Book 2018 – 2021 report of the committee on infectious diseases, 31st Edition.
[5]
Medecins Sans Frontiers. Clinical guidelines – Diagnosis and treatment Manuel. 2016 Edition. ISBN 978 -2-37585-001-5.
[6]
Chowell G., Shin E., Braver F., Diaz – Duenas P., Hyman J. M. and Castillo – Chavez C. (2005) Modeling the transmission dynamics of acute haemorrhagic conjunctivitis: Application to the 2003 outbreak in Mexico. Stat. Med 25(11): 1840 – 1857.
[7]
Unyong B., Naowarat S., (2014) Stability Analysis of Conjunctivistis model with nonlinear incidence term. Australian Journal of Basic and Applied Sciences. 8(24): 52 – 58.
[8]
Suratchala S., Anake S., Surapol N. (2015) Effect of education Campaign on Transmission model of conjunctivistis. Australian J. B. and App. Sc. 9(7): 811 – 815.
[9]
Sireepatch Sangsawang, Tareerat T., Mannissa M., Puntani P. (2012) Local stability Analysis of mathematical model for heamorrhagic conjunctivistis Disease. KMITL Sci. Tech. J. 12(2): 189 – 197.
[10]
Van den Driessche P., Watmough J. (2002) Reproduction numbers and sub – threshold endemic equilibrium for compartmental models of disease transmission. Math. Biosc. 180: 29 – 48.
[11]
Robert M. M. (1973) Stability and Complexity in model ecosystem. United States of America. Princeton University press.
[12]
Okosun K. O., Rachid O., Marcus N. (2013) Optical Control Strategies and coeffectiveness analysis of a malaria model. Biosys. 111(2): 83 – 101.
[13]
Lenhart S., Workman J. T. (2007) Optimal control Applied to Biological Models. Chapman and Hall CRC, London.
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