using optimal control to treat osteoclast

Metastasis occurs when cancerous cells move from their original location to otherareas of the body. one of the areas where the metastasis is to be made is bone. in this paper wedescribe the special case of bone metastasis, called osteolysis, and then survey how the diseaseis controlled from the mathematical point of view.✓ motivation or purpose: the purpose of this paper is to find the optimal use of medicationto minimize the tumor volume by using optimal control.method: : considering the drug used in the medical area for this disease, we will studythe effect the drug on the model and simulate the nonlinear partial differential equationsmodel, by using discretization and a combination algorithm.✓ results: : the simulation results show that using medication based on the obtainedresponse from optimal control to cure tumor concentrations, the tumor density will bereduced compared to the drug - free model.✓ conclusions: : the results show that after the use of drugs, the patient’s condition isreturned to a state where the metastasis is beginning and is not yet advanced, in fact themetastasis is inhibited, which is beneficial to the patient.