Stability analysis of fractional order mathematical model of tumor-immune system interaction

Abstract

Abstract In this paper, a fractional-order model of tumor-immune system interaction has been considered. In modeling dynamics, the total population of the model is divided into three subpopulations: macrophages, activated macrophages and tumor cells. The effects of fractional derivative on the stability and dynamical behaviors of the solutions are investigated by using the definition of the Caputo fractional operator that provides convenience for initial conditions of the differential equations. The existence and uniqueness of the solutions for the fractional derivative is examined and numerical simulations are presented to verify the analytical results. In addition, our model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. Numerical simulations are given for different choices of fractional order α and the obtained results are compared with the experimental data. The best approach to reality is observed around α = 0.80 . One can conclude that fractional model best fit experimental data better than the integer order model.