A mathematical model of cancer treatment by immunotherapy

• Published in: Mathematical biosciences Vol. 163; no. 2; pp. 159 - 199
• Main Authors: Nani, Frank, Freedman, H.I.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.02.2000; Elsevier Science
• Subjects: Antineoplastic agents; Biological and medical sciences; Brain Neoplasms - immunology; Brain Neoplasms - therapy; Cancer treatment; Competition; Dynamic modelling; Female; Hopf bifurcation; Humans; Immunotherapy; Immunotherapy, Adoptive; Interleukin-2 - therapeutic use; Killer Cells, Lymphokine-Activated - immunology; Medical sciences; Models, Biological; Neoplasm Metastasis; Neoplasms - immunology; Neoplasms - pathology; Neoplasms - therapy; Ovarian Neoplasms - immunology; Ovarian Neoplasms - therapy; Periodicity; Persistence and extinction; Pharmacology. Drug treatments; Stability; Competition; Stability; Dynamic modelling; Cancer treatment; Immunotherapy; Persistence and extinction; Periodicity; Hopf bifurcation; Equilibrium state; Treatment; Action principle; Malignant tumor; Mathematical model; Tumor cell
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/S0025-5564(99)00058-9

In this paper, a detailed mathematical study of cancer immunotherapy will be presented. General principles of cancer immunotherapy and the model equations and hypotheses will be discussed. Mathematical analyses of the model equations with regard to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, persistence, extinction and global stability will be analyzed. It will also be shown that bifurcations can occur, and criteria for total cure will also be derived.