Impulsive control dosing BCG immunotherapy for non-muscle invasive bladder cancer

Abstract

This article provides a solution for a control system derived from a mathematical model of four ordinary differential equations that describe the dynamics between the bacillus Calmette-Guerin (BCG) vaccine concentration, immune-system and tumor cells in non-muscle invasive bladder cancer. Generally, in cancer treatments, such as immunotherapies, the problems of administration procedures, do not take place through continuous injections of clinical agents in the diseased organs, but are often referred to therapeutic optimization problems with pulse vaccinations. For our study, we discuss the advantages of BCG immunotherapy when it is administered as a sequence of pulsed instillations in the bladder. We include numerical simulations based on the variational equation method resolved using a fourth-order iterative Runge–Kutta scheme combined with an optimization technique that computes the gradient of the objective function to find the optimal vaccination times and BCG dosage amounts.