A mathematical model of cancer treatment by immunotherapy

Mathematical Biosciences

Volumn 163, Issue 2, 2000, Pages 159-199

  Nani, Frank ^a   Freedman, H I ^a,b  

^a Appl Math Inst 632 Ctrl A   (Canada)

^b SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Cancer treatment; Competition; Dynamic modelling; Hopf bifurcation; Immunotherapy; Periodicity; Persistence and extinction; Stability

Indexed keywords

TUMOR ANTIGEN;

ADOPTIVE IMMUNOTHERAPY; ARTICLE; CANCER CELL; CANCER IMMUNOLOGY; CANCER IMMUNOTHERAPY; HUMAN; HUMAN CELL; IMMUNE SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL;

BRAIN NEOPLASMS; FEMALE; HUMANS; IMMUNOTHERAPY, ADOPTIVE; INTERLEUKIN-2; KILLER CELLS, LYMPHOKINE-ACTIVATED; MODELS, BIOLOGICAL; NEOPLASM METASTASIS; NEOPLASMS; OVARIAN NEOPLASMS;

EID: 0034087591     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(99)00058-9     Document Type: Article

References (31)

1. DeVita V.T., Hellman S., Rosenberg S.A. Biologic Therapy of Cancer. 1995;J.B. Lippincott, Philadelphia.
2. A.C. Hollinshead, Immunotherapy cancer: the outlaw cell, in: R.E. LaFond (Ed.), Amer. Chem. Soc., 1988, p. 237.
3. McCluskey J.et al. The biology of antigen processing and presentation. McCluskey J.M. Antigen Processing and Recognition. 1991;1 CRC, London.
4. Toledo-Pereya L.H. Immunology Essentials for Surgical Practice. 1988;PSG, Littletone, MA.
5. Wanebo H.J., Leong S.P.L. Immunobiology of the cancer patient: Current topics. Toldeo-Pereya L.H. Immunology Essentials of Surgical Practice. 1989;59 PSG, Littleton, MA.
6. Merrill S.J. A model of the role of natural killer cells in immune surveillance. Int. J. Math. Biol. 12:1981;363.
7. Yoshida R., Zanadi Z.A. Circulating immune complexes in patients with neoplastic disorders. Oncology. 37:1980;152.
8. R.H. Goldfarb, M.A. Baker et al., (Abstract), Chemoimmunotherapy with IL-2 activated NK cells including the use of zyn-linked doxorubicin, Nat. Immun. (1996/97) 168.
9. D. Herlyn, Koprowski, Anti-idiotypic antibodies in cancer therapy, in: A.C. Bona (Ed.), Biological Applications of Anti-Idiotypes, vol. II, 1986, p. 123.
10. Soiffer R.J., Chapman P.B.et al. Administration of R24 monoclonal antibody and low dose interleukin-2 for malignant melanoma. Clin. Cancer Res. 3:1997;17.
11. H.C. Stevenson, Adoptive Cellular Immunotherapy of Cancer, Marcel Dekker, New York, 1989.
12. M. Hagenaars, U. Nannmark et al., (Abstract), Kinetics of tumor infiltration by adoptively transferred A-NK cells: Implications for the mechanisms behind anti-tumor effects, Nat. Immun. (1996/97) 168.
13. R.B. Herberman, P. Basse et al., Immunotherapy with A-NK cells and IL-2, Nat. Immun. (1996/97) 168.
14. Rees R.C. The Biology of Clinical Applications of Interleukin-2. 1990;Oxford University, Oxford, London.
15. S.A. Rosenberg, Adoptive immunotherapy for cancer, Sci. Am., (May 1990) 62.
16. Rosenberg S.A., Lotze M., Muul L.et al. Observations on the systemic administration of autologous lymphokine activated killer cells (LAK) and recombinant interleukin-2 (r-IL2) to patients with metastatic cancer. N. Engl. J. Med. 313:1985;1485.
17. Rosenberg S.A. Lymphokine activated killer (LAK) cells: A new approach to immunotherapy of cancer. J. Nat. Cancer Inst. 75:1985;595.
18. Kalland T., Belfrage H.et al. Analysis of the murine lymphokide-activated killer (LAK) cell phenomenon: Dissection of effectors and progenitors into NK and T like cells. J. Immunol. 138:1987;3640.
19. Caligiuri M.A., Murray C., Robertson M.J.et al. Selective modulation of human natural killer (NK) cells in viro after prolonged infusion of low dose recombinant interleukin-2 (rIL-2). J. Clin. Invest. 91:1993;123.
20. Konrad M.W., Hemstreet G.et al. Pharmocokinetics of recombinant interleukin-2 (rIL-2) in humans. Cancer Res. 50:1990;2009.
21. Freedman H.I., Rai B. Can mutualism alter competitive outcome? A mathematical analysis. Rocky Mountain J. Math. 25:1995;217.
22. Freedman H.I., Mathsen R. Persistence of predator-prey systems with ratio-dependent predator influence. Bull. Math. Biol. 55:1993;817.
23. Freedman H.I., Ruan S. Hopf bifurcation in three-species food chain models with group defense. Math. Biosci. 111:1992;73.
24. H.I. Freedman, B. Rai, Persistence in a predator-prey-competitor-mutualist model, in: M. Farkas, V. Kertesz, G. Stepan (Eds.), Proceedings of the Eleventh International Conference on Non-linear Oscillations, Janos Bolyai Math. Soc., Budapest, 1987, p. 73.
25. Butler G.J., Freedman H.I., Waltman P. Uniformly persistent systems. Proc. Am. Math. Soc. 96:1986;425.
26. Eves H. Elementary Matrix Theory. 1966;Dover, New York.
27. J.P. LaSalle, The Stability and Control of Discrete Processes, Springer, Berlin, 1986, pp. 1-40.
28. LaSalle J., Lefchetz S. Stability by Liapunov's Direct Method. 1961;Academic Press, New York.
29. n , vol. 39, Springer, Berlin, New York, 1984.
30. Freedman H.I., Waltman P. Persistence in models of three competitive populations. Math. Biosci. 73:1984;89.
31. Wiggins S. Introduction to Applied Non-Linear Dynamical Systems and Chaos. 1990;Springer, New York.