Optimal control analysis of combined chemotherapy-immunotherapy treatment regimens in a PKPD cancer evolution model


  • Anuraag Bukkuri University of Minnesota




Mathematical oncology, dynamical systems, optimal control


The author constructs a mathematical model capturing tumor-immune dynamics, incorporating the evolution of drug resistance, pharmacokinetics and pharmacodynamics of administered drugs, and immunotherapy possibilities. Numerical simulations are performed to analyze the model under a variety of treatment possibilities. A sensitivity analysis is performed to determine the parameters contributing the most to the variance in effector cell, resistant, and sensitive tumor cell populations. Then, a detailed optimal control analysis is performed, along with a numerical simulation of optimal treatment profiles for a hypothetical patient.


Birkhead BG, Rankin EM, Gallivan S, Dones L, Rubens RD (1987). A Mathematical Model of the Development of Drug Resistance to Cancer Chemotherapy. Eur. J. Cancer Clin. Oncology, 23(9), 1421-1427.

Bukkuri A (2019). Optimal control analysis of combined anti- angiogenic and tumor immunotherapy. Open Journal of Mathematical Sciences, 3, 349-357.

L. G. de Pillis, W. Gu, and A. E. Radunskaya (2006). Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations. Journal of Theoretical Biology, 238(4):841–862.

Athanassios Iliadis and Dominique Barbolosi (2000). Optimizing Drug Regimens in Cancer Chemotherapy by an Efficacy–Toxicity Mathematical Model

V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson (1994). Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56(2): 295—321.

Lai X, Friedman A (2017). Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model. PLoS ONE 12(5)

Liao KL, Bai XF, Friedman A (2014). Mathematical modeling of interleukin-27 induction of anti-tumor T cells response. PLoS ONE 9(3)

Zhang XY, Trame MN, Lesko LJ, Schmidt, S (2015). Sobol Sensitivity Analysis: A Tool to Guide the Development and Evaluation of Systems Pharmacology Models. CPT Pharmacometrics Syst. Pharmacol. 4, 69-79.

Elbarbary RA, Miyoshi K, Myers JR, Du P, Ashton JM, Tian B, Maquat LE (2017). Tudor-SN-mediated endonucleolytic decay of human cell microRNAs promotes G1/S phase transition.; Science (New York, N.Y.); Vol 356(6340).

Burden T, Ernstberger J, Fister R (2004). Optimal Control Applied to Immunotherapy. Discrete and Continuous Dynamical Systems, 4(1), 135–146.

Fister R, Lenhart S, McNally J (1998). Optimizing Chemotherapy in an HIV , Elec. J.DE., 32, 1–12.






Original Articles