Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects
Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects
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Date
2018
Authors
Appiagyei, Ebenezer
Osman, Mojeeb AL-Rahman EL-Nor
Kibona, Isack E.
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Publisher
Journal of Scientific Research & Reports
Abstract
In this paper, we propose a SEIR-SEI optimal control model of malaria transmission with standard
incidence rate. We present four control strategies to prevent the prevalence of infection in the
society. In order to do this, we introduce an optimal control problem with an objective function,
where the four control functions, prevention using Long-Lasting Insecticide Treated Net(LLITN)
u1(t), the control effort on malaria treatment of infected individuals u2(t), the insecticide spray on
the breeding grounds for the mosquito u3(t), the prevention using Indoor Residual Spraying u4(t),
have been used as control measures for exposed and infected individuals. We show the existence
of an optimal control pair for the optimal control problem and derive the optimality conditions. Our
numerical simulation suggests that the two controls strategies u1(t) and u2(t) are more effective
than the other control strategies in controlling (reducing) the number of exposed and infected
individuals and also in increasing the number of recovered individuals
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Citation
Osman, M. A., Ebenezer, A., & Kibona, I. E. (2018). Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects. Journal of Scientific Research and Reports, 20(3), 1-16.