International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 5, Issue 6, 2017, PP 1-19 ISSN 2347-307X (Print) & ISSN 2347-3142 (Online) DOI: http://dx.doi.org/10.20431/2347-3142.0506001 www.arcjournals.org International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Page 1 Quantum Optimal Control Dynamics for Delay Intracellular and Multiple Chemotherapy Treatment (MCT) of Dual Delayed HIV - Pathogen Infections Bassey, E. Bassey * * Department of Mathematics /Statistics, Cross River University of Technology, Calabar, Nigeria 1. INTRODUCTION Considered as the most dreaded transmittable infection with no known cogent medical cure, the human immunodeficiency virus (HIV), which often transmute to terminal irreversible manifestation – the acquired immunodeficiency syndrome (AIDS) have posed a challenging treat to the scientific world. The amiable quest of tackling this life threatening disease – HIV/AIDS infection has been through the application of mathematical modeling, which allows the utilization of significant knowledge of numerical methods for the optimization of host target immune system cells and the minimization of systemic cost, while suppressing viral victors below detectable clinical assay, see for examples the studies of models [1- 4]. Furthermore, following the emerging new cases of multiplicity of HIV and its allies of pathogenic infections, it has become more unsafe and agreeably incomplete to mathematically and biological model eradication of HIV/AIDS infections without accounting for the epidemiological and biological behavior of the consequences of allying pathogenic infections. The seeming varying positive contributions from numerical methods in the dynamics of single strain HIV infection have considerably been extended to the diagnosis of the epidemiological and biological behaviors of dual HIV-pathogen infectivity as has been exemplified by models [5-9]. Consequentially, the varying results from these later models have been of immense importance in subduing the tenacity of the surging cases of dual viral infectivity. Application of quantum locally optimal algorithm of successive approximation as a concept of numerical methods, which accounted for the mathematical simulations of human immune systems problems using varying optimization control strategies for immune processes and HI-virus infections were adequately Abstract: In furtherance to the pursuit for the advent of more précised and acceptable preventive and suppressive approach to the continual de-replication of viral load and parasitoid-pathogen with presupposed maximization of both CD4 + T-lymphocytes and cytotoxic T-lymphocytes (CTLs), this present study using ordinary differential equation, formulated a set of nonlinear complex 10-Dimensional mathematical dynamic dual HIV-pathogen model. In addition to the embedded dual infectivity, the novelty of this present work is in the incorporation of the crucial role of delay intracellular and immune effectors response in the presence of multiple chemotherapeutic treatments. Presenting the model as an optimal control problem and saddle with terminal time objective functional, classical Hamilton-Pontryagin function was explored in the analysis of derived quantum locally optimal algorithm of successive approximation for healthy CD4 + T cells concentration. Using Runge-Kutter of order of precision 4 in a Mathcad surface, numerical validity of the model was conducted. Results of accompanying numerical simulations indicated the maximization of both healthy CD4 + T-lymphocytes and CTLs as a function of multiple chemotherapies with high toxicity and the presence of boosted immune effectors response under reduced systemic cost. Furthermore, maximal suppression of sensitive (infected T-cells and virions) state variables, which are daunted by persistent resistive infectious components suggests for a more articulated dual infectivity model. Keywords: Dual-HIV-Pathogen-Infection, Delay-Intracellular, Multiple-Chemotherapy, Quantum-Optimal- Control, Successive-Approximation, Sensitive-State-Variable, Resistive-State-Variable. *Corresponding Author: Bassey, E. Bassey, Department of Mathematics /Statistics, Cross River University of Technology, Calabar, Nigeria