Stage-dependent models in immunology. Application to modeling the dynamics of HIV-1 infection in the lymph node

A mathematical model of the development of HIV-1 infection in a single lymph node is considered when an individual is infected with a small number of virions - mature viral particles. Target cells for virions are represented by a population of CD4+ T-lymphocytes at rest (phase G0 of the cell cycle). The dynamics of HIV-1 infection is considered within a few days after infection of an individual. The mathematical foundations necessary for constructing and studying the model in the form of a system of delay differential equations and initial data of a special type are formulated. An expression was found for the indicator R0 – the basic reproductive number. A semi-implicit Euler scheme is used to conduct computational experiments. The results of computational experiments with the model depending on the values of the indicator R0 are presented. These results are supplemented by the results of a study of a stochastic continuous-discrete model, which indicate a significant difference in the behavior of solutions of the two models.