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Optimal Control Model for Dual Treatment of Delayed Type-II Diabetes Infection in Human Population
Current Issue
Volume 7, 2019
Issue 1 (March)
Pages: 34-49   |   Vol. 7, No. 1, March 2019   |   Follow on         
Paper in PDF Downloads: 22   Since May 9, 2019 Views: 984   Since May 9, 2019
Bassey Echeng Bassey, Department of Mathematics/Statistics, Cross River University of Technology, Calabar, Nigeria.
Following the seeming insurmountable medical cure for the dreaded type-II diabetes, several and concurrent notable scientific research works for the most appropriate approach for the treatment and management of the aforementioned disease have been on the increase. In this paper, using ordinary differential equations, we formulated a set of pent-linear mathematical type-II diabetes dynamic model. The novelty of investigation was primed by a tri-linear optimal maximization of model predominant state variables following methodological application of designated bilinear control functions in the presence of incorporated time delay lag. With the derived model, the system invariant and boundedness of solutions as well as stability analysis was scientifically investigated. To achieve study set goal, the model was transformed to an optimal control problem and analysis performed using classical Pontryagin’s maximum principle. The system optimal characterization, existence of an optimal control pair and optimality system were comprehensively established. Numerical illustrative examples were then conducted. The result that follows conspicuously indicated a pragmatic flow of the model as evidenced by highly tri-linear maximization and sequence reversion of type-II diabetes’ early infection stages. Moreso, the near zero reduction of chronic type-II diabetes infection was a further affirmation of model ingenuity, which is a step towards achieving bioscientific and biotechnological height needed for this 21st century. Suggested therefore, is a more chemotherapy inclusive and possible extensively articulated method for a possible eradication of this dreaded type-II diabetes.
Hyperglycemia, Hypoglycemia, Multifactorial-Infection, Optimal-Control-Function, Penalty-Multiplier, Tri-Linear-Maximization, Type-II-Diabetes
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