Mathematical Modelling and Analysis of System of Tumor – Immune Interaction by Differential Transform Method

Abstract

Mathematical modelling is been very powerful tool to developed the tumor cell interaction and plays vital role in treatment is well. This paper reflects some research outcome tumor growth model solved by using differential transform method (DTM). Using accumulated data we take a look at possible models for the growth of cancer cells, incorporating the positive effect of the immune system. We then include the effects of chemotherapy. The presence of chemotherapy and the immune system is represented by parameters in our model. We use the differential transform method (DTM), which is an analytical method for solving a wide variety of differential equations and usually gets the solution in a series form. We have used MAPLE software for plotting of graph. We will finally show that if the concentration of chemotherapy drug is incorrect or if the drug has the incorrect toxicity, we can actually have a large growth in the number of tumor cells or a dangerous decrease in the number of effector cells.