On Optimal Control Pair Treatment: Clinical Management of Viremia Levels In Pathogenic-Induced HIV-1 Infections
Journal Title: Biomedical Journal of Scientific & Technical Research (BJSTR) - Year 2017, Vol 1, Issue 2
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 (HI- virus 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. Continue challenges posed by the lack of précised cure for the human immunodeficiency virus (HIV), leading to evolution of the acquired immunodeficiency syndrome (AIDS), is an inevitable fatal condition, which has attracted significant number of mathematical and optimal control problem models. The complexities of HIV infection progression have often deprived a better understanding of its activity in the collapse of the immune system. Furthermore, the mechanism of HIV and its multi-facets associated pathogeneses can be viewed from set point of viruses attack on CD4+ T cells and other body functioning organism, which mainstay orchestrate natural immune response to pathogenic attack [1,2]. In-view of the above constraint, most modeling now focuses on best approach to overcome all distortion to consistent suppression of the HI-virus and elimination of any associated pathogens. Thus, the study of the dynamics of HIV infection has stepped to a more importantly, multifacets infectivity and the various immunotherapies associated with its treatments. Immunotherapy administration during early stage of the disease progression is most beneficial for the raising CD4+ T cells count [3]. Understanding the impact of these immunotherapies in the dynamics of HI-virus interaction with the host immune system can better be outlined by its percentage impacts on the CD4+ T callas evaluated by the parameters associated with infection progression. The quantitative method by which we analyze this whole lot of progression is known to be through optimal control theory. Mathematical models [4-6] studied control problems of HIV infections in varying modeling approaches, using single drug treatment and similar objective functional. Optimal therapeutic control modeling for immune system response was investigated by [7]. The model used linear optimal state evaluator in a feedback therapy to minimize the effect of measurement error. Model [2], had illustrated through mathematical modeling, the effects of cytokine interleukin-2 (IL- 2) treatment on an HIV - infected patient leading to a better understanding of immune-viral dynamics necessary to produce typical disease dynamics. Also, accounting for time dependent uncertainties as its novelty, the model [8] uses stochastic optimal control theory to develop protocols for the treatment of pathogenic diseases. Optimal control strategy for a fully determined HIV model existed as a mathematical method for the clinical testing and monitoring of HIV/AIDS diseases [9]. The model demonstrated the CD4+ T cell measurement and viral load count, using reverse transcriptase inhibitor (RTI) as single treatment. An ordinary differential system were explored in modeling the interaction of the HIV virus and the immune system of the human body, with the optimal control represented as percentage effect, which the chemotherapy has on the interaction of the CD4+T cells with the virus was examined by [5]. Explore by the model [3], were two treatment controls on a single infection (HIV), one as immune booster and the other as delay in viral progression. In our earlier model [10], we had studies the impact of sustainability of low level viremia as a preventive measure for tackling virological failure. These two later models form the framework for this present study. In this paper, using ordinary differential equation, we propose and formulate a classical improve 3-Dimensional mathematical model, as against existing 2-Dimensional model [3], which accounts for the optimal benefits based on the maximization of the immune system and the dynamic optimal cost of pair treatment of two infectious variables - HIV virus and parasitoid-pathogen. The model which deploy optimal control theory, is aim at studying the bi-linear interaction of two infectious variables on the immune system, with pair control immunotherapies (reverse transcriptase inhibitor - RTI and protease inhibitor PI), as treatment strategies. Explore in the model, is the utilization of Pontryagin's Maximum Principle in the analysis of the derived model and then presuppose the existence and uniqueness of the model solution and results numerically illustrated using Runge Kutter of order of precision 4 in a MathCAD environment. Therefore, the study which holistically deploy optimal control techniques, is aim at investigating a set model underline by increase in healthy cells concentration, suppression and elimination of viruses at a minimal pair treatment cost, as a clinical approach in the sustainability of low level viremia.
Authors and Affiliations
Bassey E
Keywords
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- EP ID EP567432
- DOI 10.26717/BJSTR.2017.01.000204
- Views 201
- Downloads 0
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