Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools

Michael Uchenna; Offia Akachukwu; Elebute Kafayat

doi:doi:10.11648/j.acm.20190802.11

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Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools

Michael Uchenna, Offia Akachukwu, Elebute Kafayat

Published in Applied and Computational Mathematics (Volume 8, Issue 2)

Received: 12 March 2019 Accepted: 15 April 2019 Published: 15 May 2019

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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.

Published in	Applied and Computational Mathematics (Volume 8, Issue 2)
DOI	10.11648/j.acm.20190802.11
Page(s)	29-36
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Conjunctivitis, Stability, Optimal Control, Mathematical Model

References

[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, 31^st 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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Michael Uchenna, Offia Akachukwu, Elebute Kafayat. (2019). Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Applied and Computational Mathematics, 8(2), 29-36. https://doi.org/10.11648/j.acm.20190802.11

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Michael Uchenna; Offia Akachukwu; Elebute Kafayat. Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Appl. Comput. Math. 2019, 8(2), 29-36. doi: 10.11648/j.acm.20190802.11

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AMA Style

Michael Uchenna, Offia Akachukwu, Elebute Kafayat. Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Appl Comput Math. 2019;8(2):29-36. doi: 10.11648/j.acm.20190802.11

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@article{10.11648/j.acm.20190802.11,
  author = {Michael Uchenna and Offia Akachukwu and Elebute Kafayat},
  title = {Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools},
  journal = {Applied and Computational Mathematics},
  volume = {8},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.acm.20190802.11},
  url = {https://doi.org/10.11648/j.acm.20190802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20190802.11},
  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.},
 year = {2019}
}

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TY  - JOUR
T1  - Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools
AU  - Michael Uchenna
AU  - Offia Akachukwu
AU  - Elebute Kafayat
Y1  - 2019/05/15
PY  - 2019
N1  - https://doi.org/10.11648/j.acm.20190802.11
DO  - 10.11648/j.acm.20190802.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20190802.11
AB  - 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.
VL  - 8
IS  - 2
ER  -

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Author Information

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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Plain Text BibTeX RIS

APA Style

Michael Uchenna, Offia Akachukwu, Elebute Kafayat. (2019). Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Applied and Computational Mathematics, 8(2), 29-36. https://doi.org/10.11648/j.acm.20190802.11

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ACS Style

Michael Uchenna; Offia Akachukwu; Elebute Kafayat. Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Appl. Comput. Math. 2019, 8(2), 29-36. doi: 10.11648/j.acm.20190802.11

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AMA Style

Michael Uchenna, Offia Akachukwu, Elebute Kafayat. Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools. Appl Comput Math. 2019;8(2):29-36. doi: 10.11648/j.acm.20190802.11

Copy | Download

@article{10.11648/j.acm.20190802.11,
  author = {Michael Uchenna and Offia Akachukwu and Elebute Kafayat},
  title = {Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools},
  journal = {Applied and Computational Mathematics},
  volume = {8},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.acm.20190802.11},
  url = {https://doi.org/10.11648/j.acm.20190802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20190802.11},
  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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools
AU  - Michael Uchenna
AU  - Offia Akachukwu
AU  - Elebute Kafayat
Y1  - 2019/05/15
PY  - 2019
N1  - https://doi.org/10.11648/j.acm.20190802.11
DO  - 10.11648/j.acm.20190802.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20190802.11
AB  - 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.
VL  - 8
IS  - 2
ER  -

Copy | Download