Optimal control for a bone metastasis with radiotherapy model using a linear objective functional

Radiation is known to cause genetic damage highly proliferative cells such as cancer cells. However, the radiotherapy effects bone not completely known. In this work we present a mathematical modeling framework test hypotheses related radiation-induced on metastasis. Thus, pose an optimal control problem based Komarova model describing interactions between and at single site of remodeling. The treatment included in form functional which minimizes use radiation using penalty function. Moreover, are interested ‘on’ ‘off’ time states schedules; so propose with L 1 -type objective functional. Bang-bang or singular arc solutions obtained solutions. We characterize both types explicitly give necessary optimality conditions for them. numerical simulations analyze different possible also evaluate more significant parameters shift from bang-bang solution vice versa. Additionally, study fractionated that yields output resembles intermittent scheduling.