Applied Mathematics and Physics
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Applied Mathematics and Physics. 2017, 5(2), 61-76
DOI: 10.12691/amp-5-2-5
Open AccessArticle

### Optimal Control Model for Pair Chemotherapy Treatment with Time-delay Immunity in Dual HIV-Infectivity

1Cross River University of Technology, Calabar 540252, Nigeria

Pub. Date: June 16, 2017

Cite this paper:
Bassey E. Bassey. Optimal Control Model for Pair Chemotherapy Treatment with Time-delay Immunity in Dual HIV-Infectivity. Applied Mathematics and Physics. 2017; 5(2):61-76. doi: 10.12691/amp-5-2-5

### Abstract

The seeming incurable status of HIV/AIDS and its associated virus infectivity had continuously led to series of scientific research, geared towards the amelioration of the increasing trend of the deadly disease. In this paper, a system of ordinary differential equations was used for the formulation of a 4-Dimensional mathematical dynamic HIV-pathogen model. The model was presented as optimal control problem, which accounted for the methodological pair chemotherapy treatment, with treatment factors clinically sandwiched in two temporal time-delay immunity chambers. The methodology of the model involved dual state infectious variables, pair treatment factors - reverse transcriptase inhibitors and protease inhibitors (RTI and PI), with immune system cells as vectors. The study explored numerical methods with analysis conducted using classical Pontryagin’s Maximum Principle. We proved that the model variables have non-negative solutions and as well, established the existence and uniqueness of the optimal control strategy, which led to the derivation of the model optimal dynamic solution. Numerical computations of the model explored Runge-Kutter of order of precision 4 in a Mathcad environment. The result demonstrated novel precision, which not only agreeing with known existing models but also showed that the higher the amount of optimal weight factor, the earlier, efficient, faster and less amount of chemotherapies required for the maximization of healthy CD4+ T cell count concentration. Furthermore, sustainability of declined infectivity and significant minimization of optimal cost was a function of prolong treatment schedule with drug validity period accounted for. Therefore, the study which could be readily adopted for other infectious diseases, suggests further investigations with more interplay of multiple control functions.

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