Mathematical modeling of the initial period of spread of HIV-1 infection in the lymphatic node

A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.