Mathematical Model Of The Interaction Between Cytotoxic T Lymphocytes And Hiv

Abstract

In this thesis work we developed a mathematical model to describe the dynamics of the interaction between Cytotoxic T Lymphocytes and HIV. The resulting model is a system of non-linear ordinary di erential equations. In this thesis, we prove existence and uniqueness as well as positivity and boundedness of the solutions to the system of di erential equations. In addition, we derive the reproduction numbers, and analyze the local stability of the di erential equation model. From the analytical solution and numerical simulations we observe that if the reproduction number is less than the solution converges to the disease free stead state, while if the reproduction number is greater than the solution converges to endemic equilibrium point and the infection cannot cleared.