Optimal control of educational campaign applied to the transmission of trachoma disease: a mathematical model
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Optimal control of educational campaign applied to the transmission of trachoma disease: a mathematical model Ogunmiloro Oluwatayo Michael1 Received: 28 March 2020 / Revised: 15 October 2020 / Accepted: 17 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents a mathematical model describing the transmission of trachoma disease in human host population. The model is analyzed in a feasible region and the basic reproduction number (Rtr ) of trachoma epidemic is obtained to show that if Rtr < 1, the model system at the fixed trachoma-free equilibrium is locally and globally asymptotically stable. An optimal control of educational campaign strategy is imposed on the model system to investigate the impact of education campaign control on the sub-population of the total human host population towards minimizing trachoma infection by initiating compliance to healthy behavior in the human host community. The existence and uniqueness and the characterization of the optimal control model analysis is carried out, while the optimality system is derived and solved using the finite difference scheme in the absence and presence of control. The results reveal that varying the control parameter at u = 0.5 and u = 0.9 shows that the maximum coverage is attained within few days before declining to the lower bound in one month. This further shows that the initiation of positive behavior and strict compliance to educational instructions through campaign is effective in minimizing trachoma in human host community. Keywords Trachoma · Reproduction number · Optimality system · Local stability · Global stability Mathematics Subject Classification 92B05 · 49K20 · 49K40
1 Introduction Trachoma is a debilitating ocular disease affecting the global world population with the dreadful impact most felt in subSaharan Africa, where Nigeria is one of the countries in Africa with highest number of human individuals affected by trachoma. Information available in World Health Organization (WHO) fact sheet of 2019 [1] reveal that, 2.2 million people have ocular problems and 1.2 million went blind due to trachoma. Also, an estimated 7.3 million individuals require preventive surgery against trachiasis [2]. Trachoma infection is contacted directly and indirectly through the discharge of pus from the eyes, nose, and infected environmental sources like water sources, pit laterine, used towels and cloths etc. Associated clinical symptoms are eye pain, light sensitivity, discharge of pus in the eye and so on.
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Ogunmiloro Oluwatayo Michael [email protected] Department of Mathematics, Ekiti-State University, Ado-Ekiti, Ekiti-State, Nigeria
The goal of WHO is to develop a strategy called SAFE (Surgery to treat, Antibiotics, Facial cleanliness, Environmental improvement) to eradicate trachoma by 2020 [3]. Umar et al. [4] and Alada et al. [5] surveyed and investigated the high prevalence of trachoma in Taraba and Kogi states of Nigeria. As part of the global trachoma mapping project, Mypet et al
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