Modelling of the tumor growth under oncolytic virotherapy with piecewise differential operators: The effects of combinations of specialist viruses

This study proposes to modify a mathematical model of virotherapy inducing cytokine IL-12 and co-stimulatory molecule 4-1BB ligand release with the concept of piecewise derivatives with the aim of analyzing the effects of treatment combinations on tumor growth. In addition to the equilibrium points for the tumor model, the solutions of the model have been proven to be positive. For the model under investigation, the basic reproduction number has been calculated to examine the transmission potential of oncolytic viruses. A method based on Newton polynomial is presented for the numerical solution of the model with piecewise derivative and the numerical simulations for piecewise model has been depicted for different values of fractional orders.Simulations show that viral oncolytic plays a crucial role in reducing tumor size but an increase in stimulation of cytotoxic T cells can lead to a short-term reduction followed by a more rapid relapse. Furthermore, thanks to the model modified with the concept of piecewise derivative to examine the effects of using different doses at different times on tumor growth, it has been possible to conclude that the virus dose given at the time when the tumor size started to increase after the first dose caused a decrease in tumor size. Finally, according to the assumptions of the considered model and the outputs of the mathematical tools used, it can be concluded that tumor growth seems to be controllable through treatment combinations in virotherapy.