Abstract
The communication is devoted to investigation of some properties of a mathematical model describing the response of the immunological system of a vertebrate to infection caused by foreign antigen. The model is formulated as a system of ordinary differential equations [1], [2], [3]. A new numerical algorithm based on non-standard finite differences [4], [5] is proposed. The qualitative properties of the numerical scheme are analyzed. Results of numerical experiments are presented and discussed from computational and biological view points. [1] M. A. Nowak, C. R. Bangham, Population dynamics of immune responses to persistent viruses , Science 272 (5258) (1996) 74--79. [2] R. J. De Boer, A. S. Perelson, Target cell limited and immune control models of HIV infection: a comparison , Journal of Theoretical Biology 190 (3) (1998) 201--214. [3] D. Wodarz, Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology, Springer, New York, 2007 [4] R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific Publishing, Singapore, 1994 [5] D. T. Dimitrov, H. V. Kojouharov, B. M. Chen-Charpentier, Reliable finite difference schemes with applications in mathematical ecology , in: R. E. Mickens (Ed.), Advances in the Applications of Nonstandard Finite Difference Schemes, World Scientific Publishing, Singapore, 2005, 249--285
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