Generalized Kinetic Theory Approach to Modeling Spread and Evolution of Epidemics

Mathematical and Computer Modelling

Volumn 39, Issue 1, 2004, Pages 1-12

  Delitala, M ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Epidemics; Generalized Boltzmann equation; Kinetic models; Nonlinearity; Population dynamics

Indexed keywords

EID: 0842310301     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(04)90501-8     Document Type: Article

References (24)

1. C. Cercignani, R. Illner and M. Pulvirenti, Theory and Application of the Boltzmann Equation, Springer, Heidelberg, (1993).
2. C. Croizet and R. Gatignol, Boltzmann like modelling of a suspension, Math. Models Meth. Appl. Sci. 12, 943-964, (2002).
3. P.E. Jabin, Various levels of models for aerosols, Math. Models Meth. Appl. Sci. 12, 903-922, (2002).
4. N. Bellomo and M. Pulvirenti, Editors, Modeling in Applied Sciences: A Kinetic Theory Approach, Birkhäuser, Boston, MA, (2000).
5. E. De Angelis and L. Mesin, On the kinetic (cellular) theory. Conceptual frameworks on modelling the immune response, Math. Models Meth. Appl. Sci. 11, 1609-1630, (2001).
6. E. De Angelis and P. Jabin, Analysis of a mean modelling of tumor and immune system competition, Math. Models Meth. Appl. Sci. 13, 187-206, (2003).
7. B. Carbonaro and N, Serra, Towards mathematical models in psychology: A stochastic description of human feelings, Math. Models Meth. Appl. Sci. 12, 1467-1502, (2002).
8. M. LoSchiavo, The modelling of political dynamics by generalized kinetic (Boltzmann), Mathl. Comput. Modelling 37 (3/4), 261-281, (2003).
9. N. Bellomo, V. Coscia and M. Delitala, On the mathematical theory of vehicular traffic flow I - Fluid dynamic and kinetic modeling, Math. Models Meth. Appl. Sci. 12, 1801-1844, (2002).
10. D. Helbing, Traffic and related self-driven many-particle systems, Review of Modern Physics 73, 1067-1141, (2001).
11. N. Bellomo and M. LoSchiavo, Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models, World Scientific, London, (2000).
12. N. Bellomo and M. Pulvirenti, Guest Editors, Special Issue on the Modeling in Applied Sciences by Methods of Transport and Kinetic Theory, Special issue of Math. Models Meth. Appl. Sci. 12, 911-1058, (2002).
13. L. Arlotti, N. Bellomo and M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Phys. 29, 125-139, (2000).
14. L. Arlotti, N. Bellomo and E. DeAngelis, Generalized kinetic (Boltzmann) models: Mathematical structures and applications, Math. Models Meth. Appl. Sci. 12, 579-604, (2002).
15. O. Diekmann and J.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases, Wiley, New York, (2000).
16. E. Geigant, K. Ladizhansky and A. Mongilner, An integro differential model for orientational distributions of F-actin cells, SIAM J. Appl. Math. 59, 787-809, (1998).
17. T. Hillen and H. Othmer, The diffusion limit of transport equations derived from velocity jump processes, SIAM J. Appl. Math. 61, 751-775, (2000).
18. T. Hillen, Hyperbolic models for chemosensitive movement, Math. Models Meth. Appl. Sci. 12, 1007-1034, (2002).
19. L. Papiez and V. Tulovsky, A stochastic model of the evolution derived from elastic velocity processes with diffusion-jump characteristics, Math. Models Meth. Appl. Sci. 12, 921-942, (2002).
20. N. Bellomo and A. Bellouquid, From a class of kinetic models to the macroscopic equations for multicellular systems in biology, Discrete and Cont. Dynam. Systems B (to appear).
21. M. Lachowicz, From microscopic to macroscopic description for general kinetic models, Math. Models Meth. Appl. Sci. 4, 59-80, (2004).
22. K. Latrach, Compactness results for transport equations and applications, Math. Models Meth. Appl. Sci. 11, 1181-1202, (2001).
23. S. Mischler, B. Perthame and L. Ryzhik, Stability in a nonlinear population maturation model, Math. Models Meth. Appl. Sci. 12, 1751-1772, (2002).
24. K. Latrach and A. Zeghal, Existence results for a boundary value problem arising in growing cell populations, Math. Models Meth. Appl. Sci. 13, 1-18, (2003).