A Comparative Study for Mathematical Modelling of the Contest of CAR-T and Tumour Cells in Solid Cancers Using Fractional- and Integer-Order Derivatives

Abstract

Cancer is a disease resulting from the fractious growth and division of abnormal cells and has gotten consistent and dedicated attention from scientists across multiple disciplines. To date, several mathematical studies have been done to study its dynamics. In this paper, we study two fractional-order mathematical models that describe the competition between CAR-T and tumour cells in terms of their immune-suppressive efficiency. We explore whether the use of a large number of CAR-T cells encountering the antigens of solid tumours could beat the immune-suppressive force of cancer. Our results are obtained through the implementation of the well-known Caputo fractional derivative as well as the Adams-Bashforth-Moulton scheme. The main aim of this study is to compare the results we obtained through the use of fractional derivatives with previously published integer-order simulations. Of interest are the instances when the results obtained via the fractional-order derivative contradict the solutions provided by the integer-order models.