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In this paper, we analyse the structure of equations in the earlier proposed mathematical model of the dynamics of age-related changes in population of peripheral T lymphocytes. To investigate behaviour of the model solutions in a wide range of values of variables we introduce a linear relation between the rate constants of T lymphocytes proliferation and the values of the mean length of telomeric chromosome fragments spent by naive and memory cells in the course of immune response, as well as the dependence of these parameters on the value of the cell replicative potential. We obtain sufficient conditions for existence, uniqueness, and positiveness of solutions over the whole time interval. The results of numerical calculations illustrate the capabilities of the model for describing accelerated aging mechanisms of the immune system using the example of HIV infection.

Immune system aging may be affected by HIV infection: the mathematical model of immunosenescence