Mathematical Modeling Of The Interaction Between Langerhans Cells And The Spread Of Hiv Infection

Abstract

In this research work, we propose a system of nonlinear ordinary di erential equation used to model the interaction between Langerhans cells and HIV infection. The model consists of ve compartments, namely, susceptible Langerhans cells, infected Langerhans cells, susceptible T-cells, infected T-cells and free HIV particles. The biology of inter- actions of Langerhans cells with HIV and a mathematical preliminaries which plays a crucial role in our entire research work were described. Also, the existing model which focuses on representing the long term dynamics of the interaction between T-cells and HIV infection was studied to assist us in formulating our model system. By presenting a theoretical framework related to the infection mechanism, a biologically meaning full assumption were considered. Furthermore, the positivity of the model solution, the equi- librium point (both virus free and endemic equilibrium) of the model was shown and it's stability was investigated. Finally, by using a numerical simulation the developed model was studied and the results concluded that the numerical simulation matches the analytical solution as expected.