Applied and Computational Mathematics 2019; 8(2): 29-36 http://www.sciencepublishinggroup.com/j/acm doi: 10.11648/j.acm.20190802.11 ISSN: 2328-5605 (Print); ISSN: 2328-5613 (Online) Control Model on Transmission Dynamic of Conjunctivitis During Harmattan in Public Schools Michael Uchenna, Offia Akachukwu, Elebute Kafayat Department of Mathematics, Alex Ekwueme Federal University Ndufu Alike, Ikwo, Abakaliki, Nigeria Email address: 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 Received: March 12, 2019; Accepted: April 15, 2019; Published: May 15, 2019 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 1. Introduction Lately 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. In modeling of infectious diseases, it helps in estimating the threshold parameters, elucidation of the transmission dynamics, in addition to its ability to provide feasible control strategies [1]. 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]. 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 infection is transmitted from an infected person to a susceptible individual through contact with discharge from conjunctivae or upper respiratory tracts of infected persons, contact with contaminated foreign bodies that has been in contact with the eyes. It can also be transmitted vertically to newly born babies due to its direct relation between maternal gonococcal and chlamydial infection. We are interested in conjunctivitis caused by virus rather called Acute Hemorrhagic conjunctivitis (ADC). The incubation period of ADC ranges from 1 – 3 days. The symptoms of the infection include tearing, irritation, photophobia, sore throat which usually results in swelling of the lids or purulent discharges [4]. Conjunctivitis infection is commonly contracted in the