How to mathematically optimize drug regimens using optimal control

J Pharmacokinet Pharmacodyn. 2018 Feb;45(1):127-137. doi: 10.1007/s10928-018-9568-y. Epub 2018 Feb 6.


This article gives an overview of a technique called optimal control, which is used to optimize real-world quantities represented by mathematical models. I include background information about the historical development of the technique and applications in a variety of fields. The main focus here is the application to diseases and therapies, particularly the optimization of combination therapies, and I highlight several such examples. I also describe the basic theory of optimal control, and illustrate each of the steps with an example that optimizes the doses in a combination regimen for leukemia. References are provided for more complex cases. The article is aimed at modelers working in drug development, who have not used optimal control previously. My goal is to make this technique more accessible in the biopharma community.

Keywords: Combination therapy; Constrained optimization; Control theory; Disease modeling; Optimal control.

MeSH terms

  • Anti-HIV Agents / administration & dosage
  • Antineoplastic Combined Chemotherapy Protocols / administration & dosage
  • Dose-Response Relationship, Drug*
  • HIV Infections / drug therapy
  • Humans
  • Leukemia, Myelogenous, Chronic, BCR-ABL Positive / drug therapy
  • Models, Biological*
  • Pharmacology / methods*
  • Treatment Outcome


  • Anti-HIV Agents