Numerical Modeling of the Dynamics of HIV-1 Infection and T-cell Immune Response in the Lymph Node

A mathematical model describing the dynamics of HIV-1 infection development in a single lymph node of an infected individual taking into account to the T-cell immune response is constructed and studied. CD4+ T-lymphocytes, macrophages, and dendritic cells are target cells for virions. The model takes into account contacts of target cells with virions and local intercellular interactions, as a result apear latently infected cells and cells producing viral particles. The development of the T-cell immune response is the result of the contact interaction of CD8+ T-lymphocytes and antigen-presenting cells. The model is a high-dimensional system of differential equations with delay supplemented with initial data. The existence and uniqueness of the solution of the model and the non-negativity of the solution components on the semi-axis for given non-negative initial data are shown. An algorithm for numerical solution of the model based on the semi-implicit Euler scheme is described. The results of a computational experiment on fitting the model solutions to known experimental data in the acute phase of HIV-1 infection are presented. The flows of virions and latent infected cells from the lymph node are numerically studied depending on the ratio of the model parameters reflecting the intensity of contact interactions of virions with macrophages, dendritic cells and naive CD4+ T-lymphocytes.