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A dynamic model of non-lineal time-dependent ordinary differential equations(ODE) has been applied to the interactions of a HIV infection with the immunesystem cells. This model has been simplified into two compartments: lymph nodeand peripheral blood. The model includes CD4 T-lymphocytes in several states(quiescent Q, naive N and activated T), cytotoxic CD8 T-cells, B-cells anddendritic cells. Cytokines and immunoglobulins specific for each antigen (i.e.gp41 or p24) have been also included in the model, modelling the atractioneffect of CD4 T-cells to the infected area and the reduction of virusconcentration by immunoglobulins. HIV virus infection of CD4 T-lymphocytes ismodelled in several stages: before fusion as HIV-attached (H) and after fusionas non-permissive / abortively infected (M), and permissive / latently infected(L) and permissive / actively infected (I). These equations have beenimplemented in a C++/Python interface application, called Immune System app,which runs Open Modelica software to solve the ODE system through a 4th orderRunge-Kutta numerical approximation. Results of the simulation show thatalthough HIV virus concentration in both compartments is lower than $10^{-10}$virus/$\mu L$ after t=2 years, quiescent lymphocytes reach an equilibrium witha concentration lower than the initial conditions, due to the latency state,which serves as a reservoir in time of virus production. As a conclusion, thismodel can provide reliable results in other conditions, such as antiviraltherapies.

Dynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review