Anuradha Devi, Aditya Ghosh
Department of Mathematics
Royal Group of Institutions
Opp. Balaji Temple and ISBT
Betkuchi, Guwahati, Assam, 781035,INDIA

Abstract. A mathematical model is presented that describes growth of the tumor cells and intrinsic behaviour of it in the presence of immune cells. Two models considered here are:

• Immune-Tumor growth model(I-T Model)
• Immune-Tumor-Drug Model(I-T-D Model)

Both I-T and I-T-D models are highly non-linear in nature. The effect of growth of these cells on normal cells have not been considered. In presence of both cells the model behave as a competing model. Constant number of immune cells are assumed to be present in the system. In the absence of tumor cells, the immune cells will not be stimulated to grow and these leads to a natural death of immune cells. Immune-Tumor-Drug(I-T-D) is a modified version of Immune-Tumor(I-T) model which incorporate the effect of drug administered assuming that drug kills both tumor and immune cells at different rates.

Stability of both models have been analyzed under various equilibrium conditions.

Received: March 26, 2012

AMS Subject Classification: 92B05, 90-08, 65L07, 65L06

Key Words and Phrases: mathematical model, tumor cell, immune cell, drug, eigenvalue, stability

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