Qualitative analysis of a nonlinear integrodifferential equation modeling tumor-host dynamics

Mathematical and Computer Modelling

Volumn 23, Issue 6, 1996, Pages 11-29

  Arlotti, L ^a   Lachowicz, M ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

Dynamical systems; Kinetic theory; Tumor immune systems

Indexed keywords

EID: 0003005010     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/0895-7177(96)00017-9     Document Type: Article

References (15)

1. N. Bellomo and G. Forni, Dynamics of tumor interaction with host immune system, Mathl. Comput. Modelling 20 (1), 107-122 (1994).
2. N. Bellomo, G. Forni and L. Preziosi, On a kinetic (cellular) theory for the competition between tumors and host immune system, J. Biolog. Systems (to appear).
3. F. Hoppensteadt, Mathematical Theories of Populations: Demographics, Genetics and Epidemics, SIAM Reg. Conf. Ser. No. 20, SIAM, (1975).
4. K. Dietz and K.P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol. 26, 1-25 (1988).
5. K.P. Hadeler, Pair formation models with maturation period, J. Math. Biol. 32, 1-15 (1993).
6. U. an der Heiden and M.C. Mackey, The dynamics of production and destruction: Analytic insight into complex behavior, J. Math. Biol. 16, 75-101 (1982).
7. O. Dieckmann, M. Gyllenberg and H. Thieme, Perturbing semigroups by solving Stieltjes renewal equations, Differ. Integral Equ. 6, 155-181 (1993).
8. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, (1990).
9. L. Arlotti and N. Bellomo, Population dynamics with stochastic interaction, Transport Theory Statist. Phys. (to appear).
10. N. Bellomo and M. Lachowicz, Mathematical biology and kinetic theory: Evolution of the dominance in a population of interacting organisms, In Kinetic Theory and Hyperbolic Systems, (Edited by V. Boffi et al.), pp. 11-20, World Sci., (1992).
11. N. Bellomo and M. Lachowicz, A Liapunov functional and dissipativity analysis for a kinetic model in mathematical biology, Ricerche Mat. 41, 65-76 (1992).
12. T.C. Gard, Introduction to Stochastic Differential Equations, Dekker, (1987).
13. P. Hartman, Ordinary Differential Equations, Birkhäuser, (1982).
14. L. Pontryagin, Ordinary Differential Equations, Addison-Wesley, (1962).
15. R. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, J. Wiley, (1976).