Therapy strategy in tumour cells and immune system interaction mathematical model

References

• Stepanova NV. Course of the immune reaction during the development of a malignant tumour. Biophysics. 1980;24:917–923.
   Google Scholar
• Martin RB, Fisher ME, Minchin RF, et al. A mathematical model of cancer chemotherapy with an optimal selection of parametrs. Math. Biosci. 1990;99:205–230.
   PubMed Web of Science ®Google Scholar
• de Vladar HP, Gonzalez JA. Dynamic response of cancer under the influence of immunological activity and therapy. J. Theor. Biol. 2004;227:335–348.
   PubMed Web of Science ®Google Scholar
• d’Onofrio A, Ledzewicz U, Maurer H, et al. On optimal delivery of combination therapy for tumors. Math. Biosci. 2009;222:13–30.
   PubMed Web of Science ®Google Scholar
• Kuznetsov V, Makalkin I, Taylor M, et al. Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. B. Math. Biol. 1994;56:295–321.
   PubMed Web of Science ®Google Scholar
• Frascoli F, Kim PS, Hughes BD, et al. A dynamical model of tumour immunotherapy. Math. Biosci. 2014;253:50–62.
   PubMed Web of Science ®Google Scholar
• Roesch K, Hasenclever D, Scholz M. Modeling lymphoma therapy and outcome. Bull. Math. Biol. 2014;76:401–430.
   PubMed Web of Science ®Google Scholar
• Kirschner P, Panetta JC. Modeling immunotherapy of the tumor--immune interaction. J. Math. Biol. 1998;37:235–252.
   PubMed Web of Science ®Google Scholar
• Wilson S, Levy D. A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy. Bull. Math. Biol. 2012;74:1485–1500.
   PubMed Web of Science ®Google Scholar
• Castiglione F, Piccoli B. Cancer immunotherapy, mathematical modeling and optimal control. J. Theor. Biol. 2007;247:723–732.
   PubMed Web of Science ®Google Scholar
• de Pillis LG, Gallegos A, Radunskaya AE. A model of dendritic cell therapy for melanoma. Front. Oncol. 2013;3:56–77.
   PubMedGoogle Scholar
• Itik M, Salamci MU, Banks SP. Optimal control of drug therapy in cancer treatment. Nonlinear Anal. 2009;71:1473–1486.
   Web of Science ®Google Scholar
• Ledzewicz U, Mosalman MSF, Schaettler H. Optimal controls for a mathematical model of tumor--immune interactions under targeted chemotherapy with immune boost. Discrete Cont. Dyn. -B. 2013;18:1031–1051.
   Web of Science ®Google Scholar
• Martin RB. Optimal control drug scheduling of cancer chemotherapy. Automatica. 1992;28:205–230.
   Web of Science ®Google Scholar
• de Pillis LG, Fister KR, Gu W, et al. Seeking bang--bang solutions of mixed immuno-chemotherapy of tumors. Electr. J. Differ. Equ. 2007;2007:1–24.
   Google Scholar
• de Pillis LG, Fister KR, Gu W, et al. Optimal control of mixed immunotherapy and chemotherapy of tumors. J. Biol. Syst. 2008;16:841–862.
   Web of Science ®Google Scholar
• de Pillis LG, Fister KR, Gu W, et al. Mathematical model creation for cancer chemo-immunotherapy. Comput. Math. Method M. 2009;10:165–184.
   Web of Science ®Google Scholar
• de Pillis LG, Gu W, Radunskaya AE. Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 2006;238:841–862.
   PubMed Web of Science ®Google Scholar
• Matveev AS, Savkin AV. Application of optimal control theory to analysis of cancer chemotherapy regimens. Syst. Control Lett. 2002;46:311–321.
   Web of Science ®Google Scholar
• Bratus AS, Fimmel E, Todorov Y, et al. On strategies on a mathematical model for leukemia therapy. Nonlinear Anal.-Real. 2012;13:1044–1059.
   Web of Science ®Google Scholar
• Engelhart M, Lebiedz D, Sager S. Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function. Math. Biosci. 2011;229:123–134.
   PubMed Web of Science ®Google Scholar
• Pontryagin LS, Boltyanski VG, Gamkrelidze RV, et al. The mathematical theory of optimal processes. Moscow: Nauka; 1969.
   Google Scholar
• Moiseev NN. Computational methods in the theory of optimal systems. Moscow: Nauka; 1971.
   Google Scholar
• Vasiliev FP. Methods of optimization. Moscow: Factorial Press; 2002.
   Google Scholar
• Krylov IA, Chernousko FI. Algorithm of successive approximations for problems of optimal control. J. Comp. Math. Math. Phys. 1972;12:14–34.
   Google Scholar
• Srochko VA. Iteration methods for the solution of optimal control problems. Moscow: Fizmatlit; 2000.
   Google Scholar
• Dienfenbach A, Jensen ER, Jamieson AM, et al. Rae1 and H60 ligands of the NKG2D receptor stimulate tumor immunity. Nature. 2001;413:165–171.
   PubMed Web of Science ®Google Scholar
• Dudley ME, Wunderlich JR, Robbins PF, et al. Cancer regression and autoimmunity in patients after clonal repopulation with antitumor lymphocytes. Science. 2002;298:850–854.
   PubMed Web of Science ®Google Scholar
• Pasquier E, Kavallaris M, André N. Metronomic chemotherapy: new rationale for new directions. Nat. Rev. Clin. Oncol. 2010;7:455–465.
   PubMed Web of Science ®Google Scholar