A stochastic nominal control optimizing the adoptive immunotherapy for cancer using tumor-infiltrating lymphocytes

Allen LJ (2010) An introduction to stochastic processes with applications to biology. CRC Press, Boca Raton

Babaei N, Salamci MU (2014) State dependent riccati equation based model reference adaptive stabilization of nonlinear systems with application to cancer treatment. In: Proceedings of the 19th IFAC world congress, Cape Town, South Africa

Babaei N, Salamci MU (2015) Personalized drug administration for cancer treatment using model reference adaptive control. J Theor Biol 371:24–44

Beerenwinkel N, Schwarz RF, Gerstung M, Markowetz F (2015) Cancer evolution: mathematical models and computational inference. Syst Biol 64(1):e1–e25

Ben-Ami E, Schachter J (2015) Adoptive transfer of tumor-infiltrating lymphocytes for melanoma: new players, old game. Immunotherapy 7(5):477–479

Blattman JN, Greenberg PD (2004) Cancer immunotherapy: a treatment for the masses. Science 305(5681):200–205

Blinov N, Berjanskii M, Wishart DS, Stepanova M (2009) Structural domains and main-chain flexibility in prion proteins. Biochemistry 48(7):1488–1497

Bonadonna G, Valagussa P (1983) Chemotherapy of breast cancer: current views and results. Int J Radiat Oncol Biol Phys 9(3):279–297

Bunimovich-Mendrazitsky S, Shochat E, Stone L (2007) Mathematical model of BCG immunotherapy in superficial bladder cancer. Bull Math Biol 69(6):1847–1870

Burden TN, Ernstberger J, Fister KR (2004) Optimal control applied to immunotherapy. Discret Contin Dyn Syst Ser B 4(1):135–146

Cardinale RM, Benedict SH, Wu Q, Zwicker RD, Gaballa HE, Mohan R (1998) A comparison of three stereotactic radiotherapy techniques; ARCS vs. noncoplanar fixed fields vs. intensity modulation. Int J Radiat Oncol Biol Phys 42(2):431–436

Castiglione F, Piccoli B (2007) Cancer immunotherapy, mathematical modeling and optimal control. J Theor Biol 247(4):723–732

Cheney E, Kincaid D (2012) Numerical mathematics and computing. Cengage Learning, Boston

Cimen T (2008) State-dependent Riccati equation (SDRE) control: a survey. In Proceedings of the 17th world congress of the international federation of automatic control (IFAC), Seoul, Korea, July pp 6–11

Couzin-Frankel J (2013) Cancer immunotherapy. Science 342(6165):1432–1433

Darcy PK, Neeson PJ (2015) Adoptive immunotherapy: a new era for the treatment of cancer. Immunotherapy 7(5):469–471

De Pillis LG, Gu W, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 238(4):841–862

Dutcher J (2002) urrent status of interleukin-2 therapy for metastatic renal cell carcinoma and metastatic melanoma. Oncology (Williston Park, NY) 16(11 Suppl 13):4–10

Ehrenberg M, Elf J, Aurell E, Sandberg R, Tegner J (2003) Systems biology is taking off. Genome Res 13(11):2377–2380

Elmouki I, Saadi S (2014) BCG immunotherapy optimization on an isoperimetric optimal control problem for the treatment of superficial bladder cancer. Int J Dyn Control. doi:10.1007/s40435-014-0106-5

Elmouki I, Saadi S (2015) Quadratic and linear controls developing an optimal treatment for the use of BCG immunotherapy in superficial bladder cancer. Opt Control Appl Methods 37(1):176–189

Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–1186

Gattinoni L, Powell DJ, Rosenberg SA, Restifo NP (2006) Adoptive immunotherapy for cancer: building on success. Nat Rev Immunol 6(5):383–393

Ghaffari A, Nazari M, Arab F (2015) Suboptimal mixed vaccine and chemotherapy in finite duration cancer treatment: state-dependent Riccati equation control. J Braz Soc Mech Sci Eng 37(1):45–56

Grewal MS, Andrews AP (2014) Kalman filtering: theory and practice with MATLAB, 4th edn. Wiley, Hoboken

Hamdache A, Saadi S, Elmouki I, Zouhri S (2013) Two therapeutic approaches for the treatment of HIV infection in AIDS stage. Appl Math Sci 7(105):5243–5257

Hamdache A, Elmouki I, Saadi S (2014) Optimal control with an isoperimetric constraint applied to cancer immunotherapy. Int J Comput Appl 94(15):31–37

Hamdache A, Saadi S, Elmouki I (2015) Nominal and neighboring-optimal control approaches to the adoptive immunotherapy for cancer. Int J Dyn Control. doi:10.1007/s40435-015-0205-y

Herskovic A, Martz K, Al-Sarraf M, Leichman L, Brindle J, Vaitkevicius V, Emami B (1992) Combined chemotherapy and radiotherapy compared with radiotherapy alone in patients with cancer of the esophagus. N Engl J Med 326(24):1593–1598

Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Fluids Eng 83(1):95–108

Kirschner D, Panetta JC (1998) Modeling immunotherapy of the tumorimmune interaction. J Math Biol 37(3):235–252

Kirschner D, Tsygvintsev A (2009) On the global dynamics of a model for tumor immunotherapy. Math Biosci Eng 6(3):573–583

Ladyzhenskaya OA, Solonnikov VA, Uralceva NN (1968) Linear and quasilinear equations of parabolic type, translations of mathematical monographs, vol 23. American Mathematical Society, Providence

Lenhart S, Workman JT (2007) Optimal control applied to biological models. CRC Press, Boca Raton

Ludwig D (1974) Stochastic population theories, lecture notes in biomathematics, vol 3. Springer, Berlin

Luzyanina T, Bocharov G (2014) Stochastic modeling of the impact of random forcing on persistent hepatitis B virus infection. Math Comput Simul 96:54–65

Ma J, Protter P, Yong J (1994) Solving forward–backward stochastic differential equations explicitly: a four step scheme. Probab Theory Relat Fields 98(3):339–359

Ma J, Yong J (1999) Forward–backward stochastic differential equations and their applications. Springer, Berlin

Ma J, Yong J (1995) Solvability of forward-backward SDEs and the nodal set of HJB equations. Chin Ann Math 16:279–298

MacCheever MA (2008) Twelve immunotherapy drugs that could cure cancers. Immunol Rev 222(1):357–368

Marino P, Preatoni A, Cantoni A (1995) Randomized trials of radiotherapy alone versus combined chemotherapy and radiotherapy in stages IIIa and IIIb nonsmall cell lung cancer. A meta-analysis. Cancer 76(4):593–601

McAsey M, Mou L, Han W (2012) Convergence of the forward–backward sweep method in optimal control. Comput Optim Appl 53(1):207–226

Meyer GH (1973) Initial value methods for boundary value problems. Academic Press, New York

Mukhopadhyay B, Bhattacharyya R (2009) A nonlinear mathematical model of virus-tumor–immune system interaction: deterministic and stochastic analysis. Stoch Anal Appl 27(2):409–429

Naidu DS (2002) Optim Control Syst, vol 2. CRC Press, Boca Raton

Nazari M, Ghaffari A (2015) The effect of finite duration inputs on the dynamics of a system: proposing a new approach for cancer treatment. Int J Biomath 8(03):1550036

Nazari M, Ghaffari A, Arab F (2015) Finite duration treatment of cancer by using vaccine therapy and optimal chemotherapy: state-dependent Riccati equation control and extended Kalman filter. J Biol Syst 23(01):1–29

Peng S (1990) A general stochastic maximum principle for optimal control problems. SIAM J Control Optim 28(4):966–979

Peng S, Wu Z (1999) Fully coupled forward–backward stochastic differential equations and applications to optimal control. SIAM J Control Optim 37(3):825–843

Pontryagin LS (1987) Mathematical theory of optimal processes. CRC Press, Boca Raton

Raj A, Van Oudenaarden A (2009) Single-molecule approaches to stochastic gene expression. Annu Rev Biophys 38:255270

Reid WT (1972) Riccati differential equations. Mathematics in science and engineering, vol 86. Academic Press, Cambridge

Ricciardi LM (1977) Diffusion processes and related topics in biology. Springer, Berlin

Rosenberg SA (2008) Overcoming obstacles to the effective immunotherapy of human cancer. Proc Natl Acad Sci 105(35):12643–12644

Rosenberg SA, Restifo NP, Yang JC, Morgan RA, Dudley ME (2008) Adoptive cell transfer: a clinical path to effective cancer immunotherapy. Nat Rev Cancer 8(4):299–308

Rosenberg SA, Yang JC, Restifo NP (2004) Cancer immunotherapy: moving beyond current vaccines. Nat Med 10(9):909–915

Rosenberg SA, Restifo NP (2015) Adoptive cell transfer as personalized immunotherapy for human cancer. Science 348(6230):62–68

Rosenberg SA, Spiess P, Lafreniere R (1986) A new approach to the adoptive immunotherapy of cancer with tumor-infiltrating lymphocytes. Science 233(4770):1318–1321

Rumelin W (1982) Numerical treatment of stochastic differential equations. SIAM J Numer Anal 19(3):604–613

Saadi S, Elmouki I, Hamdache A (2015) Impulsive control dosing BCG immunotherapy for non-muscle invasive bladder cancer. Int J Dyn Control 3(3):313–323

Sahami F, Salamci MU (2015) Decentralized model reference adaptive control design for nonlinear systems; state dependent Riccati equation approach. In: In Carpathian Control Conference (ICCC), 2015 16th international. IEEE, pp 437–442

Samanta GP, Aiza RG, Sharma S (2015) Analysis of a mathematical model of periodically pulsed chemotherapy treatment. Int J Dyn Control. doi:10.1007/s40435-015-0204-z

Sauvage F, Pontier D (2005) Intérêts des modèles déterministes et stochastiques en épidémiologie des maladies infectieuses: Exemple du Hantavirus Puumala. Epidémiologie et Santé Animale 47:63–82

Shaffer DR, Cruz CRY, Rooney CM (2013) Adoptive T cell transfer. In cancer immunotherapy. Springer, New York, pp 47–70

Shindo Y, Hazama S, Maeda Y, Matsui H, Iida M, Suzuki N, Oka M (2014) Adoptive immunotherapy with MUC1-mRNA transfected dendritic cells and cytotoxic lymphocytes plus gemcitabine for unresectable pancreatic cancer. J Transl Med 12:175

Siddiqui I, Mantovani A, Allavena P (2015) Adoptive T-cell therapy: optimizing chemokine receptor-mediated homing of T cells in cancer immunotherapy. In cancer immunology. Springer, Berlin, pp 263–282

Starkov KE, Coria LN (2013) Global dynamics of the KirschnerPanetta model for the tumor immunotherapy. Nonlinear Anal Real World Appl 14(3):1425–1433

Starkov KE, Krishchenko AP (2014) On the global dynamics of one cancer tumour growth model. Commun Nonlinear Sci Numer Simul 19(5):1486–1495

Stefanovic S, Schuetz F, Sohn C, Beckhove P, Domschke C (2014) Adoptive immunotherapy of metastatic breast cancer: present and future. Cancer Metastasis Rev 33(1):309–320

Stengel RF, Ghigliazza RM, Kulkarni NV (2002) Optimal enhancement of immune response. Bioinformatics 18(9):1227–1235

Stengel RF (1994) Optimal control and estimation. Dover Publications, Mineola

Trelat E (2005) Controle optimal: theorie et applications. Vuibert, Paris

Trotter MV, Krishna-Kumar S, Tuljapurkar S (2013) Beyond the mean: sensitivities of the variance of population growth. Methods Ecol Evol 4(3):290–298

Uzzo RG, Novick AC (2001) Nephron sparing surgery for renal tumors: indications, techniques and outcomes. J Urology 166(1):6–18

Whitmore WF (1956) Hormone therapy in prostatic cancer. Am J Med 21(5):697–713

Xiong J (2008) An introduction to stochastic filtering theory. Oxford University Press, Oxford

Xue D, Chen Y (2008) Solving applied mathematical problems with MATLAB. CRC Press, Boca Raton

Yong J, Zhou XY (1999) Stochastic controls: hamiltonian systems and HJB equations, stochastic modelling and applied probability, vol 43. Springer, New York

Yong J (2002) Stochastic optimal control and forward–backward stochastic differential equations. Comput Appl Math 21:369–403

Zhang J (2004) A numerical scheme for BSDEs. Ann Appl Probab 14(1):459–488

Zill D, Wright W (2012) Differential equations with boundary-value problems. Cengage Learning, Boston

Zouhri S, Saadi S, Elmouki I, Hamdache A, Rachik M (2013) Mixed immunotherapy and chemotherapy of tumors: optimal control approach. IJCSI Int J Comput Sci Issues 10(4):1