Discrete kinetic cellular models of tumors immune system interactions

Mathematical Models and Methods in Applied Sciences

Volumn 6, Issue 8, 1996, Pages 1187-1209

  Lo Schiavo, M ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3242872325     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/s021820259600050x     Document Type: Article

References (22)

1. J. A. Adam, Diffusion models of prevascular and vascular tumor growth - A review, in Mathematical Population Dynamics, eds. O. Arino et al. (Dekker, 1991).
2. J. A. Adam and R. Noren, Equilibrium model of a vascularized spherical carcinoma with central necrosis - Some properties of the solution, Math. Biosci. 33 (1993) 735-745.
3. Eds. J. A. Adam and N. Bellomo, Survey of Models for Tumor-Immune System Dynamics (Birkhaüser, 1996).
4. N. Bellomo and G. Forni, Dynamics of tumor interaction with the host immune system, Math. Comp. Modelling, 20 (1994) 107-122.
5. N. Bellomo, G. Forni and L. Preziosi, On the kinetic (cellular) theory of the competition between tumors and immune host system, in Models of Tumor Immune System Dynamics, eds. J. Adam and N. Bellomo (Birkhaüser, 1996).
6. N. Bellomo, G. Forni and L. Preziosi, On a kinetic (cellular) theory for the competition between tumors and host-immune system, J. Biol. Systems, to appear.
7. N. Bellomo and L. Preziosi, Modelling Mathematical Methods and Scientific Computation (CRC Press, 1995).
8. M. Chaplain and N. F. Britton, On the concentration profile of a growth inhibitory factor in multicell spheroids, Math. Biosci. 115 (1993) 233-245.
9. M. Chaplain, D. Benson and P. K. Maini, Nonlinear diffusion and growth inhibitory factor in multicell spheroids, Math. Biosci. 121 (1994) 1-13.
10. M. Chaplain, A vascular growth, angiogenesis, and vascular growth, in solid tumors: the mathematical modelling of stages of tumor developments, Math. Comp. Modelling - Special Issue on Modelling Tumor Immune System Dynamics, ed. N. Bellomo 23 (1996) 47-88.
11. Eds. W. Den Otter and E. J. Ruitenberg, Tumor Immunology. Mechanisms, Diagnosis, Therapy (Elsevier 1987).
12. Eds. G. Forni, R. Foa, A. Santoni and L. Frati, Cytokine Induced Tumor Immunogeneticity (Academy Press, 1994).
13. Eds. I. Green, S. Cohen and R. McCluskey, Mechanism of Tumor Immunity (J. Wiley, 1977).
14. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, 1983).
15. M. W. Hirsh and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra (Academy Press, 1974).
16. V. A. Kustnetsov, Dynamic of Immune Processes during Tumor Growth (Nauka, 1992).
17. S. Michelson and J. T. Leith, Autocrine and paracrine growth factors in tumor growth, Bull. Math. Biol. 53 (1991) 639-656.
18. S. Michelson and J. T. Leith, Growth factors and growth control of etherogeneous cell populations, Bull. Math. Biol. 55 (1993) 993-1011.
19. M. Marusic, Z. Bajzer, J. P. Freyer and S. Vuk-Pavlovic, Modelling autostimulation of growth in multicellular tumor spheroids, Internat. J. Biomed. Comp. 149 (1991) 149-158.
20. M. Marusic and S. Vuk-Pavlovic, Prediction power of mathematical models for tumor growth, J. Biol. Systems 1 (1993) 69-78.
21. G. J. V. Nossal, Life, death, and the immune system, Scientific Amer. 269 (1993) 53-72.
22. G. G. Steel, Growth Kinetics of Tumors (Clarendon, 1977).