On Optimal Control Pair Treatment: Clinical Management of Viremia Levels In Pathogenic-Induced HIV-1 Infections

DOI: 10.26717/BJSTR.2017.01.000204

Received: June 21, 2017;   Published: July 31, 2017

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Abstract

The quest to actively draw the attention of research scientist to alternative approach for the eradication of the menace of HIV and its associated pathogens, informed the decision of this present work. In this paper, we concentrated in the formulation of a set of classical improved 3-Dimensional mathematical model, using ordinary differential systems for the study of bi-linear interactions of two infectious variables (HIvirus and parasitoid-pathogen) with the human immune system, in the presence of multiple control pair treatment for the management and sustainability of low level viremia. The model were presented as an optimization control problem, primed by the maximization of uninfected CD4+ T cell count concentration under a minimized systemic cost, defined by the percentage of immunotherapies administered within a finite time interval. The method of analysis explored classical numerical methods known as Pontryagin’s Maximum Principle, which led to establishment of model optimization control strategy; and the existence and uniqueness of the solution of the optimal control pair were critically viewed. Numerical computations of the model, using Runge Kutter of order 4, in a Math cad environment were demonstrated with novel precision results, which not only agreed with known existing models but also showed that the higher the amount of optimal weight factor, that enhances the toxicity of drugs; the earlier, efficient, faster and less amount of chemotherapies required for the maximization of healthy CD4+ T cell count concentration. The model justified the sustainability of low level viremia under set control chemotherapies. Thus, the methodology and use of multiple treatment factors as designed by this model is widely recommended for other related infectious diseases.

Abbreviations| Introduction| Material and Methods| Existence, Optimization control strategy and Uniqueness| Numerical Computation and Discussion| Discussion| Conclusion| Acknowledgment| References|