THERAPEUTIC RESPONSE OF OPTIMIZED THERMODYNAMIC CONTROL MODEL IN HIV DYNAMICS

Ilo, C. P., Omenyi, S. N., Dim, E. C.

Abstract: In a continued quest to permanently have a cure to HIV infection, a thermodynamic optimized control infectivity model was introduced in an adopted basic viral dynamics model. The ensued model, an Ordinary Differential Equation (ODE) was solved at two instances. First under the condition of uninfected cell (CD4+) proliferation with saturation response and secondly when there was no uninfected cell (CD4+) proliferation and saturation response with each having two series of controlled and uncontrolled dynamics. The Ordinary Differential Equation (ODE) solution method was a numerical integration that utilized explicit Runge-Kutta method in MATLAB^TMfunction ode 23. Historical drug parameters for the model were introduced to the model for simulation of the infection dynamics from day 20 to 300 for cure. The infection time course showed that in the first instant for the controlled brown series, both infected cell count (y ) and viral load (v ) were forced to die out and converge to equilibrium of 0 cellsµL and 0 copiesmL respectively, at about five (5) days after introduction of the drug control parameters that is about the twenty fifth (25th) day of infection. The uninfected cell converges to equilibrium average supply rate from thymus and taking cognizance of proliferation to about 1200(cellsμL-1 ) at about thirtieth (35th) day after introduction of control that is about the fifty fifth (55th) day of infection. The uncontrolled blue series progressed as expected. In the second instant for the controlled green series, both infected cell count (y ) and viral load (v ) were again forced to die out and converge to equilibrium of 0 cellsµL and 0 copiesmL respectively, at about five (5) days after introduction of the optimized control drug parameters that is about the twenty fifth (25th) day of infection. The uninfected cell converges to equilibrium average supply rate from thymus to have λ/δcellsµL , 1000(cellsμL-1 ) at about thirtieth (35th) day after introduction of control that is about the fifty fifth (55th) day of infection hence validating the model. The uncontrolled red series progressed as expected. This explains recovery and making up of the depreciated uninfected cell count. Combined front of interfacial energetic approach of Hamaker coefficient and spectrophotometric approach have proved effective at optimized condition in the fight against HIV. Clinical management as well as the pharmaceutical industries should adopt the method for a clinical extinction of the disease.