A mathematical tumor model with immune resistance and drug therapy: An optimal control approach

Journal of Theoretical Medicine

Volumn 3, Issue 2, 2001, Pages 79-100

  De Pillis, L G ^a   Radunskaya, A ^b  

^a HARVEY MUDD COLLEGE   (United States)

^b POMONA COLLEGE   (United States)

Author keywords

Cancer; Competition models; Immune system; Mathematical modeling; Optimal control; Population models; Tumor

Indexed keywords

ANTINEOPLASTIC AGENT;

ARTICLE; CANCER GROWTH; CLINICAL PROTOCOL; COMPETITION; CONTROLLED STUDY; DRUG PULSE THERAPY; HOST CELL; IMMUNE RESPONSE; IMMUNOCOMPETENT CELL; OSCILLATION; POPULATION MODEL; QUALITATIVE ANALYSIS; SIMULATION; STANDARD; THEORY; TUMOR CELL; TUMOR IMMUNITY; TUMOR MODEL; TUMOR VOLUME;

EID: 0035738977     PISSN: 10273662     EISSN: None     Source Type: Journal    
DOI: 10.1080/10273660108833067     Document Type: Article

References (45)

1. The dynamics of growth-factor-modified immune response to cancer growth: One-dimensional models
2. A simple mathematical model and alternative paradigm for certain chemotherapeutic regimens
3. Breast carcinoma growth rate described by mammographic doubling time and S-phase fraction: Correlations to clinical and histopathologic factors in a screened population
4. Some stochastic models of cancer metastases
5. The asymptotic behavior of a probabilistic model for tumor growth
6. A stochastic model for the evolution of cancerous tumors
7. A stochastic model for the origin and treatment of tumors containing drug-resistant cells
8. Interactions between macrophages and T-lymphocytes: Tumor sneaking through intrinsic to helper T cell dynamics
9. Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy
10. A stochastic model of mutant growth due to mutation in tumors, based on stem cell considerations
11. Cancer dormancy. VII. A regulatory role for CD8+ T cells and IFN-gamma in establishing and maintaining the tumor-dormant state
12. Immunologic approach to cancer therapy
13. The growth law of primary breast cancer as inferred from mammography screening trials data
14. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management
15. Modeling immunotherapy of the tumor-immune interaction
16. Cell kinetic modelling and the chemotherapy of cancer
17. The gross rates of growth of human mammary carcinoma
18. Bifurcation-analysis of mathematical-model of interactions between cytotoxic lymphocytes and tumor-cells - Effect of immunological amplification of tumor-growth and its connection with other phenomena of oncoimmunology
19. Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis
20. Optimal control drug scheduling of cancer chemotherapy
21. A mathematical model of cancer chemotherapy with an optimal selection of parameters
22. Characterization of a strongly immunogenic mouse leukemia line (DL811) undergoing spontaneous cure with tumor dormancy
23. Survival of leukemic cells in a dormant state following cyclophosphamide-induced cure of strongly immunogenic mouse leukemia (DL811)
24. Host response in tumor growth and progression
25. Tumor-cell vaccination induces tumor dormancy in a murine model of B-cell leukemia/lymphoma (BCL1)
26. Eblac Z tumor dormancy in bone marrow and lymph nodes: Active control of proliferating tumor cells by CD8+ immune T cells
27. Optimal control for a cancer chemotherapy problem with general growth and loss functions
28. Modelling the macrophage invasion of tumours: Effects on growth and composition
29. A mathematical model of periodically pulsed chemotherapy Tumor recurrence and metastasis in a competitive environment
30. Stimulatory effects of immune-reactions upon the growths of untransplanted tumors
31. Conversations
32. Two-stage stochastic model for carcinogenesis with time-dependent parameters
33. Using computer simulations for evaluating the efficacy of breast cancer chemotherapy protocols
34. Immune mechanisms and tumor dormancy
35. Optimal control applications in the chemotherapy of multiple myeloma
36. Optimal control analysis of a cancer chemotherapy problem
37. Some control problems for simplest differential models of proliferation cycle
38. Irregularity in scheduling of cancer chemotherapy
39. Optimal control problems arising in cell-cycle-specific cancer chemotherapy
40. Measurement and management of carcinoma of the breast
41. Evaluation of some mathematical models for tumor growth
42. User's guide for DIRCOL: A direct collocation method for the numerical solution of optimal control problems