Open Science Journal of Mathematics and Application 2019; 7(1): 34-49 http://www.openscienceonline.com/journal/osjma ISSN: 2381-4934 (Print); ISSN: 2381-4942 (Online) Optimal Control Model for Dual Treatment of Delayed Type-II Diabetes Infection in Human Population Bassey Echeng Bassey Department of Mathematics/Statistics, Cross River University of Technology, Calabar, Nigeria Email address To cite this article Bassey Echeng Bassey. Optimal Control Model for Dual Treatment of Delayed Type-II Diabetes Infection in Human Population. Open Science Journal of Mathematics and Application. Vol. 7, No. 1, 2019, pp. 34-49. Received: March 6, 2019; Accepted: April 21, 2019; Published: May 9, 2019 Abstract 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. Keywords Hyperglycemia, Hypoglycemia, Multifactorial-Infection, Optimal-Control-Function, Penalty-Multiplier, Tri-Linear-Maximization, Type-II-Diabetes 1. Introduction For decades past, among non-transmittable (though rare with family history and vertical transmission attributes) yet devastating global disease is the diabetes. Diabetes mellitus and/or type-II diabetes (of various stages) have been in existence but without the desired scientific attention required of it. However, not until 2003, when the International Diabetes Federation (IDF) estimated that the prevalence of diabetes in the world population was still 3% (5.1% for those aged 20-79 years) on the increase, which showed that over 194 million people worldwide are diabetic, most of whom live in developing countries, [1]. Furthermore, recent survey on the devastating effect of diabetes infection revealed that over 370 million of the world population is living with diabetes with 8.5% representing adult population, [2]. Yet, very sparing attention had been accorded to this steady deepened incurable disease. From the general knowledge of the disease and in particular, type-II diabetes, it is a non-curable adult-onset chronic disease condition considered as a non-insulin dependent, which adversely affects cells metabolism of body sugar. More explicitly, type-II diabetes is synonymous to either insulin resistance (causing hyperglycemia) or the incapability of the body system (the pancreas) to produce