[1]
|
H. O. Alsaab, S. Sau, R. Alzhrani, K. Tatiparti, K. Bhise, S. K. Kashaw and A. K. Iyer, PD-1 and PD-L1 checkpoint signaling inhibition for cancer immunotherapy: Mechanism, combinations, and clinical outcome, Frontiers in Pharmacology, 8 (2017), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5572324/.
doi: 10.3389/fphar.2017.00561.
|
[2]
|
R. H. Blair, D. L. Trichler and D. P. Gaille, Mathematical and statistical modeling in cancer systems biology, Frontiers in Physiology, 3 (2012), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3385354/.
doi: 10.3389/fphys.2012.00227.
|
[3]
|
R. H. Byrd, J. C. Gilbert and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming, Mathematical Programming, 89 (2000), 149-185.
doi: 10.1007/PL00011391.
|
[4]
|
K. Chin, V. K. Chand and D. S. A. Nuyten, Avelumab: Clinical trial innovation and collaboration to advance anti-PD-L1 immunotherapy, Annals of Oncology: Official Journal of the European Society for Medical Oncology, 28 (2017), 1658–1666, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5834034/.
doi: 10.1093/annonc/mdx170.
|
[5]
|
S. Halle, K. A. Keyser, F. R. Stahl, A. Busche, A. Marquardt, X. Zheng, M. Galla, V. Heissmeyer, K. Heller, J. Boelter, K. Wagner, Y. Bischoff, R. Martens, A. Braun, K. Werth, A. Uvarovskii, H. Kempf, M. Meyer-Hermann, R. Arens, M. Kremer, G. Sutter, M. Messerle and Reinhold Förster, In vivo killing capacity of cytotoxic T Cells is limited and involves dynamic interactions and T Cell cooperativity, \emphImmunity, 44 (2016), 233-245, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4846978/.
doi: 10.1016/j.immuni.2016.01.010.
|
[6]
|
L. F. Han, S. Eikenberry, C. H. He, L. Johnson, M. C. Preul, E. J. Kostelich and Y. Kuang, Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates, Mathematical Biosciences and Engineering, 16 (2019), 5307–5323, https://www.aimspress.com/fileOther/PDF/MBE/mbe-16-05-265.pdf.
doi: 10.3934/mbe.2019265.
|
[7]
|
V. R. Juneja, K. A. McGuire, R. T. Manguso, M. W. LaFleur, N. Collins, W. N. Haining, Gordon J. Freeman and Arlene H. Sharpe, PD-L1 on tumor cells is sufficient for immune evasion in immunogenic tumors and inhibits CD8 T cell cytotoxicity, The Journal of Experimental Medicine, 214 (2017), 895–904, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5379970/.
doi: 10.1084/jem.20160801.
|
[8]
|
J. Kang, S. Demaria and S. Formenti, Current clinical trials testing the combination of immunotherapy with radiotherapy, Journal for Immunotherapy of Cancer, 4 (2016), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5028964/.
doi: 10.1186/s40425-016-0156-7.
|
[9]
|
Y. Kuang, J. D. Nagy and S. E. Eikenberry, Introduction to Mathematical Oncology, CRC Press, Boca Raton, FL, 2016.
|
[10]
|
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology, 56 (1994), 295–321, https://www.sciencedirect.com/science/article/pii/S0092824005802605.
|
[11]
|
X. L. Lai and A. Friedman, Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: A mathematical model, PLoS ONE, 12 (2017), 1-24.
doi: 10.1371/journal.pone.0178479.
|
[12]
|
T. List and D. Neri, Immunocytokines: A review of molecules in clinical development for cancer therapy, Clinical Pharmacology, 5 (2013), 29–45, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3753206/.
doi: 10.2147/CPAA.S49231.
|
[13]
|
X.-Y. Meng, N.-N. Qin and H.-F. Huo, Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species, Journal of Biological Dynamics, 12 (2018), 342-374.
doi: 10.1080/17513758.2018.1454515.
|
[14]
|
E. Nikolopoulou, L. R. Johnson, D. Harris, J. D. Nagy, E. C. Stites and Y. Kuang, Tumour-immune dynamics with an immune checkpoint inhibitor, Letters in Biomathematics, 5 (2018), S137–S159.
doi: 10.1080/23737867.2018.1440978.
|
[15]
|
Z. P. Parra-Guillen, A. Janda, P. Alzuguren, P. Berraondo, R. Hernandez-Alcoceba and I. F. Troconiz, Target-mediated disposition model describing the dynamics of IL12 and IFN$\gamma$ after administration of a mifepristone-inducible adenoviral vector for IL-12 expression in mice, AAPS Journal, 15 (2013), 183–194, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3535095/.
|
[16]
|
A. Radunskaya, R. Kim and T. Woods II, Mathematical modeling of tumor immune interactions: A closer look at the role of a PD-L1 inhibitor in cancer immunotherapy, Spora: A Journal of Biomathematics, 4 (2018), 25–41, https://ir.library.illinoisstate.edu/cgi/viewcontent.cgi?article=1022&context=spora.
doi: 10.30707/SPORA4.1Radunskaya.
|
[17]
|
A. Rao and M. R. Patel, A review of avelumab in locally advanced and metastatic bladder cancer, Therapeutic Advances in Urology, 11 (2019), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6354303/.
doi: 10.1177/1756287218823485.
|
[18]
|
E. A. Saparata and L. G. Pillis, A Comparison and catalog of intrinsic tumor growth models, Bulletin of Mathematical Biology, 76 (2014), 2010–2024, https://www.ncbi.nlm.nih.gov/pubmed/25081547.
doi: 10.1007/s11538-014-9986-y.
|
[19]
|
R. Serre, S. Benzekry, L. Padovani, C. Meille, N. André, J. Ciccolini, F. Barlesi, X. Muracciole and D. Barbolosi, Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy, Cancer Research, 76 (2016), 4931–4940, http://cancerres.aacrjournals.org/content/76/17/4931.
doi: 10.1158/0008-5472.CAN-15-3567.
|
[20]
|
L. Shi, S. Chen, L. Yang and Y. Li, The role of PD-1 and PD-L1 in T-cell immune suppression in patients with hematological malignancies., Journal of Hematology and Oncology, 6 (2013), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3851976/.
doi: 10.1186/1756-8722-6-74.
|
[21]
|
S. Shi, J. Huang and Y. Kuang, Global dynamics in a tumor-immune model with an immune checkpoint inhibitor, DCDS-B, in review.
|
[22]
|
S. Simon and N. Labarriere, PD-1 expression on tumor-specific T cells: Friend or foe for immunotherapy?, \emphOncoimmunology, 7 (2017), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5739549/.
|
[23]
|
A. Stéphanou, P. Ballet and G. Powathil, Hybrid modelling in oncology: Success, challenges and hopes, (2019), https://arXiv.org/pdf/1901.05652.pdf.
|
[24]
|
A. Talkington and R. Durett, Estimating tumor growth rates in vivo, Bulletin of Mathematical Biology, 77 (2015), 1934–1954, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4764475/.
doi: 10.1007/s11538-015-0110-8.
|
[25]
|
S. G. Tan, K. F. Liu, Y. Chai, C. W.-H. Zhang, S. Gao, G. F. Gao and J. X. Qi, Distinct PD-L1 binding characteristics of therapeutic monoclonal antibody durvalumab, Protein and Cell, 9 (2018), 135-139.
doi: 10.1007/s13238-017-0412-8.
|
[26]
|
J. Tang, J. X. Yu, V. M. Hubbard-Lucey, S. T. Neftelinov, J. P. Hodge and Y. Q. Lin, The clinical trial landscape for PD1/PDL1 immune checkpoint inhibitors, Nature Reviews Drug Discovery, 17 (2018), 854-855.
doi: 10.1038/nrd.2018.210.
|
[27]
|
J. R. Wares, J. J. Crivelli, C. Yun, I. Choi, J. L. Gevertz and P. S. Kim, Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections, Mathematical Biosciences and Engineering, 12 (2015), 1237-125.
doi: 10.3934/mbe.2015.12.1237.
|
[28]
|
A. B. Warner and M. A. Postow, Combination controversies: Checkpoint inhibition alone or in combination for the treatment of melanoma?, \emphOncology, 32 (2018), 228–34, https://www.ncbi.nlm.nih.gov/pubmed/29847853.
|
[29]
|
C. X. Xu, Y. P. Zhang, P. A. Rolfe, V. M. Hernández, W. Guzman, G. Kradjian, B. Marelli, G. Qin, J. Qi, H. Wang, H. Yu, R. Tighe, K. Lo, J. M. English, L. Radvanyi and Y. Lan, Combination therapy with NHS-muIL12 and avelumab (anti-PD-L1) enhances antitumor efficacy in preclinical cancer models, Clinical Cancer Research, 23 (2017), 5869–5880, http://clincancerres.aacrjournals.org/content/23/19/5869.
doi: 10.1158/1078-0432.CCR-17-0483.
|
[30]
|
Y. Y. Yan, A. B. Kumar, H. Finnes, S. N. Markovic, S. Park, R. S. Dronca and H. Dong, Combining immune checkpoint inhibitors with conventional cancer therapy, Frontiers in Immunology, 9 (2018), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6072836/.
doi: 10.3389/fimmu.2018.01739.
|
[31]
|
D. Zamarin and M. A. Postow, Immune checkpoint modulation: Rational design of combination strategies, Pharmacology and Therapeutics, 150 (2015), 23–32, https://www.sciencedirect.com/science/article/pii/S0163725815000042.
doi: 10.1016/j.pharmthera.2015.01.003.
|