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