Russ. J. Numer. Anal. Math. Modelling, Vol. 19, No. 4, pp. 315–329 (2004) c VSP 2004 Immune system aging may be affected by HIV infection: the mathematical model of immunosenescence T. E. SANNIKOVA , S. G. RUDNEV , A. A. ROMANYUKHA , and A. I. YASHIN † Abstract — 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 inves- tigate 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 ob- tain 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. In [16], there was proposed the mathematical model of the dynamics of age-related changes in population of peripheral T lymphocytes. T lymphocytes account for most (approximately 75%) of cells in the lymphatic nodes and are responsible for the rate and amplitude of essentially all immune processes and especially antiviral immu- nity. As compared to other components of the immune defense of an organism, the changes in the T immunity system with age are most pronounced [2] and hence responsible for the rate of the immune system aging as a whole. Thus, the math- ematical model of age-related changes in the peripheral T lymphocyte population can be regarded as a model of the immune system aging. The model parameters in [16] were adjusted by the data obtained from healthy donors of various ages. This allows one, in particular, to assume the constancy of antigen load (the absence of prolonged and severe diseases) and the normal steady functioning of various subsystems and organs of the immune system during lifetime. The next logical step is an attempt to use this model for describing the immune system aging in severe and chronic diseases. The peripheral T lymphocyte population consists of cells of two types: naive T lymphocytes and memory cells. T lymphocytes that do not participate in an immune response are called naive T lymphocytes. In the course of immune response to an Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow GSP-1, 119991, Russia † Center for Demographic Studies, Duke University, Durham, NC 27708, USA The work was supported by a Grant of the President of RF for support of Young Russian Scientists and the Leading Scientific Schools of RF (SS-150.2003.1) and the Russian Foundation for Basic Research (04-01-00579).