Fractional-order models of tumor and oncolytic virus interaction incorporating the Beddington–DeAngelis functional response: Sensitivity and cost-effectiveness analysis

In this study, we propose a fractional-order tumor-oncolytic virus interaction with the functional response of Beddington and DeAngelis and its chemotherapeutic effect. The positivity and boundedness of the solution have been analyzed, and Banach’s fixed point theorem is employed to demonstrate the existence and uniqueness of the model’s solution. Conditions for the existence and stability of a steady state in the dynamics have also been established. The basic reproduction number of the model has been computed using a next-generation matrix and its sensitivity index and elasticity index with respect to model parameters have been investigated. The partial rank correlation coefficient (PRCC) method is employed to compute the global sensitivity of parameters using Latin hypercube sampling (LHC). To reduce the tumor load, we have proposed a fractional optimal control problem and established the existence of optimal controls using Pontryagin’s maximum principle. The optimal fractional control problem has been simulated with the forward–backward sweep method using the predictor–corrector scheme, and the results are compared with an uncontrolled system with controlled dynamics. The effect of single and combined controls on reducing tumor load has been discussed. The results reveal that chemotherapy enhanced by the oncolytic virus can eliminate tumor cells and in the endemic steady state, the tumor cell population decreases with decreasing fractional order derivatives. In addition to this, numerical results of state solutions have been presented for different fractional-order derivatives. Finally, a cost-effectiveness analysis of the suggested strategies has been conducted and discussed.