Mathematical Modeling of the Interaction Between Langerhans Cells and the Spread of HIV Infection

In this research work, we propose a system of nonlinear ordinary differential equation used to model the interaction between Langerhans cells and HIV infection. The model consists of five compartments, namely, susceptible Langerhans cells, infected Langerhans cells, susceptible T-cells, infected T-cells and free HIV particles. The biology of interactions of Langerhans cells with HIV and mathematical preliminaries which plays a crucial role in our entire research work was described. By presenting a theoretical framework related to the infection mechanism, a biologically meaning full assumption was considered. Furthermore, the positivity of the model solution, the equilibrium point (both virus free and endemic equilibrium) of the model was shown and its 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