THERMODYNAMICS OF IMMUNITY WITH TRANSITION ADHESION COEFFICIENT IN HIV DYNAMICS

Ilo, C. P., Nkwocha, A. C., Dim, E. C.

Abstract: Expressed and quantifiable thermodynamic adhesion coefficient representing HIV infectivity was incorporated in an adopted basic viral dynamics and thermodynamic model which is an Ordinary Differential Equation (ODE) was solved the with value of genetic factor when basic reproduction number was one at the first instance for condition of early infection and at the second instance for dynamics of later infection to show how genetic factor representing immune system fights off the disease even there was no therapeutic intervention for twenty days and four thousand days respectively. The solution approach of the Ordinary Differential Equation (ODE) was numerical integration that utilized explicit Runge-Kutta method in MATLAB^TMfunction ode 23. Historical data for the expressed adhesion coefficient was imported from relevant literature. Solutions of the of the model, that is uninfected cell (CD4+) count (x ) (cellsμL-1 ), infected cell count (y ) (cellsμL-1 ) and viral load (v ) (copiesmL-1) infection time-course of dynamics of the thermodynamics model for 20 days for the first instance and 4000 days for second instance are in line with expectation. At the first instance which is dynamics at early stage shows that as the infection was established, the viral load picked with a corresponding drop of uninfected cell count with the expected absence of the infection oscillatory dynamics due to transition condition where every dynamic is expected to maintain an equilibrium immediately infection is established. At a later stage of the infection seen in in the second instance, it is amazingly evident that even without drug intervention, the infection was being fought down by the genetic factor in the proposed model. This is clearly seen where both viral load and infected cell count kept going down, owing to the fact that genetic factor is activating the cytotoxic T lymphocytes CTL killings of the infected cells hence viral load thereby reducing their count. Uninfected cell count as expected was seen to be approaching thymus supply rate (x≅λd) approximately 1000(cellsμL-1 ), increasing steadily even without any drug intervention which is in line with the principle. This is a clear indication of genetic factor in the model at work. The result of this paper is in line with the principle, hence validate the concept of genetic factor in the expressed adhesion coefficient model and providing understanding to infection dynamics without drug intervention. The result is of very importance to clinicians and in drug formulation.