# Drug Administered Cancer Model Under One Term Delay

Volume 14, Issue 2, pp 143-150
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### Authors

Aditya Ghosh - Department of Mathematics, Royal Group of Institutions, Betkuchi, Guwahati, Assam-781035, INDIA Anuradha Devi - Department of Mathematics, Royal Group of Institutions, Betkuchi, Guwahati, Assam-781035, INDIA

### Abstract

A mathematical model is presented here that describes the growth of tumor cells and intrinsic behavior of it in the presence of immune cells. In this model we have also considered another drug variable which has the effect on both the cells. Hence it is a model for cancer that contains immune, tumor and drug. The model is highly nonlinear in nature. The effect of growth of normal cell is not considered. Constant number of immune cells is assumed to be present in the system. In this model we have considered a delay term in the growth of tumor which makes the model more realistic. We also assume that drug kills both immune cells and tumor cells simultaneously in different rate. Stability of both immune and tumor cells with and without delay has been analyzed under equilibrium condition analytically as well as numerically. It is found that the stability of the model depends on both tumor cells as well as on the delay.

### Keywords

• Mathematical model
• Tumor cell
• Immune cell
• Drug
• Stability
• Delay

•  92C50
•  65L07

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