Analytical Study of a Fractional Cancer Model with Oncolytic Virotherapy Using the Temimi–Ansari Method

We propose a fractional-order cancer virotherapy model based on Caputo derivatives to investigate the temporal interactions among tumor cells, viruses, and immune response components. The existence and uniqueness of the solutions for the proposed model are rigorously studied. The proposed model is capable of tracking the temporal dynamics of uninfected and infected cancer cells, free oncolytic virus, and several components of the immune response. To determine the analytical solutions of the resulting nonlinear fractional-order system, we utilize the Temimi–Ansari method (TAM). The convergence and accuracy of the method are confirmed via error analysis and numerical simulation carried out in MATHEMATICA. It is observed that the fractional order plays a prominent role in controlling the temporal dynamics of the cancer–virus–immune system, leading to a reduction in the number of infected cancer cells due to virotherapy. On the other hand, the immune response is vital for controlling cancer growth.