Carbon nanomaterials have received increasing attention in drug delivery applications because of their distinct properties and structures, including large surface areas, high conductivity, low solubility in aqueous media, unique chemical functionalities and stability at the nano-scale size. Particularly, they have been used as nano-carriers and mediators for anticancer drugs such as, combination with Cisplatin, Camptothecin and Doxorubicin. Cancer has become the most challenging disease because its sophisticated therapy and classified as one of the top killers according to the World health organization records. The aim of the current work is to study and investigate the mechanism of combination between single-walled carbon nanotubes (SWCNTs) and the fullerene derivatives (C N -[OH] β ) as mediators, and anticancer drugs for photodynamic therapy directly to destroy the infected cells without damaging the normal ones. Here, we obtain a bio-medical model to determine the efficiency of usefulness of Doxorubicin (DOX) as an antitumor agent conjugated with SWCNTs with variant radii r and fullerene derivative (C N -[OH] β ). The two sub-models are obtained mathematically to evaluate the potential energy arising from the DOX-SWCNT and DOX-(C N -[OH] β ) interactions. DOX modelled as two-connected spheres, small and large, each interacting with different SWCNTs (variant radii r ) and fullerene derivatives C N -[OH] β , forming based on the number of carbon atoms (N) and the number of Hydroxide molecules (OH) ( β ), respectively.