Page 117 - Control Theory in Biomedical Engineering
P. 117
Modeling and optimal control of cancer-immune system 103
de Pillis, L.G., Radunskaya, A., 2003. The dynamics of an optimally controlled tumor model:
a case study. Math. Comput. Model. 37, 1221–1244.
de Pillis, L.G., Gu, W., Radunskaya, A.E., 2006. Mixed immunotherapy and chemotherapy
of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 238 (4),
841–862.
de Pillis, L.G., et al., 2008. Optimal control of mixed immunotherapy and chemotherapy of
tumors. J. Biol. Syst. 16 (1), 51–80.
Dunn, G.P., Bruce, A., Ikeda, H., Old, L.J., Schreiber, R.D., 2002. Cancer immunoediting:
from immunosurveillance to tumour scape. Nat. Immunol. 3, 991–998.
Fleming, W.H., Rishel, R.W., 1994. Deterministic and Stochasitic Optimal Control.
Springer-Verlag, New York, NY.
Fowler, A.C., Mackey, M.C., 2002. Relaxation oscillations in a class of delay differential
equations. SIAM J. Appl. Math. 63, 299–323.
Halanay, A., 1966. Differential Equations, Stability, Oscillations, Time Lags. Academic Press,
New York, London.
Joshi, B., Wang, X., Banerjee, X., Tian, H., Matzavinos, A., Chaplain, M.A.J., 2009. On
immunotherapies and cancer vaccination protocols: a mathematical modelling approach.
J. Theor. Biol. 259 (4), 820–827.
Kim, R., Woods, T., Radunskaya, A., 2018. Mathematical modeling of tumor immune
interactions: a closer look at the role of a PD-L1 inhibitor in cancer immunotherapy.
SPORA J. Biomath. 4, 25–41.
Kirschner, D., Panetta, J.C., 1998. Modeling immunotherapy of the tumor-immune
interaction. J. Math. Biol. 37, 235–252.
Kolmanovskii, V.B., Shaikhet, L.E., 1996. Control of Systems With Aftereffect. Translation
of Mathematical Monographs, American Mathematical Society, USA.
Kuznetsov, V.A., Makalkin, I.A., Taylor, M.A., Perelson, A.L., 1994. Nonlinear dynamics of
immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math.
Biol. 56 (2), 295–321.
Lackie, J., 2010. A Dictionary of Biomedicine. Oxford University Press, Oxford.
Liu, Y., Huang, H., Saxena, A., Xiang, J., 2002. Intratumoral coinjection of two adeno-
viral vectors expressing functional interleukin-18 and inducible protein-10, respec-
tively, synergizes to facilitate regression of established tumors. Cancer Gene Ther.
9, 533–542.
Nagy, J., 2005. The ecology and evolutionary biology of cancer: a review of mathematical
models of necrosis and tumor cells diversity. Math. Biosci. Eng. 2, 381–418.
Nelson, N.W., Perelson, A.S., 2002. Mathematical analysis of delay differential equation
models of HIV-1 infection. Math. Biosci. 179, 73–94.
Neves, H., Fai Kwok, H., 2015. Recent advances in the field of anti-cancer immunotherapy.
BBA Clin. 3, 280–288.
Pontryagin, L.S., Boltyanski, R.V., Gamkrelidge, R.V., Mischenko, E.F., 1962. The
Mathematical Theory of Optimal Processes. John Wiley & Sons, New York, NY.
Preziosi, L., 2003. Cancer Modeling and Simulation. Chapman & Hall/CRC Mathematical
Biology Series (Book 3).
Rihan, F.A., 2000. Numerical Treatment of Delay Differential Equation in Bioscience
(Ph.D. thesis), The University of Manchester (UK).
Rihan, F., Velmurugan, G., 2020. Dynamics of delay differential models with arbitrary-
derivative for tumor-immune system. Chaos Solitons Fractals 132, 109592.
Rihan, F.A., Safan, M., Abdeen, M.A., Abdel-Rahman, D.H., 2012. Mathematical model-
ing of tumor cell growth and immune system interactions. Int. J. Modern Phys. 95–111.
Rihan, F.A., Abdelrahman, D., Al-Maskari, F., Ibrahim, F., 2014a. A delay differential model
for tumour-immune response and control with chemo-immunotherapy. Comput.
Math. Methods Med. 2014, 15.