Abstract:
This article presents a variable order nonlinear mathematical model and its optimal control for a Tumor
under immune suppression. The formulation generalizes the one proposed by Kim et. al. consisting of
eleven integer order differential equations. The new approach adopts a variable-order fractional model
with the derivatives defined in the Caputo sense. Two control variables, one for immunotherapy and one
for Chemotherapy, are proposed to eliminate or reduce the Tumor cells. A simple numerical technique
called the nonstandard generalized Euler method is developed to solve the proposed optimal control
problem. Moreover, the stability analysis and the truncation error are studied. Numerical simulations and
comparative studies are implemented. Our findings disclose that the proposed scheme used here has two
main advantages: it is faster than the generalized Euler scheme and it can reduce the number of Tumor
cells in a proper process better than the second scheme.