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.
Highlights
Mathematical modeling of biological processes, physical process and other epibiological processes have been on the raise, basically because of its ability to incorporate the undermining factors that are so intricate to elucidate
Mathematical modeling of infectious diseases has been productive in terms of its pragmatic therapeutic recommendations for treatment and prevention strategies of infectious diseases has been borne, and has been an alternative tool that has been in exploit in the combative approach of infectious diseases [2]
The numerical simulation is considered with the intent of obtaining the effect of control strategies on the transmission dynamics of the infection
Summary
Mathematical modeling of biological processes, physical process and other epibiological processes have been on the raise, basically because of its ability to incorporate the undermining factors that are so intricate to elucidate. Mathematical biology is a branch of mathematics that has been gaining tremendous interest of scholars recently; modeling of infectious diseases, modeling of growth in the human anatomy, body fluid modeling, and other viable areas. These surges include the solid reputation of such models in laying foundational structures to understanding the complexities of biological processes and the likes. Conjunctivitis is an infectious disease of the eye (s) that is characterized by typically redness or swelling of the white of the eye (Conjunctiva) It is most often caused by virus, bacteria, allergy or chemical irritation (Pollen, smoke, cosmetics or chlorine in water) [3]. The symptoms of the infection include tearing, irritation, photophobia, sore throat which usually results in swelling of the lids or purulent discharges [4]
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