Global existence and asymptotic behaviour for a degenerate diffusive seir model

Electronic Journal of Qualitative Theory of Differential Equations

Volumn , Issue , 2005, Pages 1-15

  Aliziane, Tarik ^a   Langlais, Michel ^b  

^a UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Asymptotic behavior; Degenerate equation; Global existence; Population dynamics; Reaction diffusion equations

Indexed keywords

EID: 14744306089     PISSN: 14173875     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2005.1.2     Document Type: Article

References (27)

1. N. Alikakos and R. Rostamian, Large time behavior of solution neumann boundary value problem of the porous medium equation, Indiana University Mathematics Journal 30 (1981), no. 5, 749-785.
2. T. Aliziane, Etude de la régularité pour un problème d'évolution dégénéré en dimension supérieure de l'espace, USTHB, Algiers, 1993.
3. T. Aliziane and M. Langlais, Global existence and periodic solution for a system of degenerate evolution equations, (preprint) Faculté de Mathématiques USTHB, 2003.
4. T. Aliziane and M. S. Moulay, Global existence and asymptotic behaviour for a system of degenerate evolution equations, Maghreb Math Rev 9 (2000), no. 1 & 2, 9-22.
5. R.M. Anderson, H.C. Jackson, R.M. May, and A.D.M. Smith, Population dynamics of fox rabies in europe, Nature 289 (1981), 765-770.
6. P. Baras, Compacité de l'opérateur f → u solution d'une équation non linéaire (du/dt) + Au ∋ f, C. R. Acad. Sc. (1978), 1113-1116.
7. S. Busenberg and K.C. Cooke, Vertically transmitted diseases, Biomathematics, vol. 23, Springer Verlag, Berlin, 1993.
8. V. Capasso, Mathematical structures of epidemic systems, Lecture Notes in Biomathematics (1993), no. 97.
9. V. Capasso and G. Serio, A generalization of the kermack-mckendrick deterministic epidemic model, Math. Biosci. 42 (1978), 41-61.
10. F. Courchamp, Ch. Suppo, E. Fromont, and C. Bouloux, Dynamics of two feline retroviruses (fix and felv) within one population of cats, Proc. Roy. Soc. London. B 264 (1997), 785-794.
11. E. DiBenedetto, Continuity of weak solutions to a general pourous medium equation, Indiana University Mathematic Journal 32 (1983), no. 1, 83-118.
12. O. Diekmann, M. C. De Jong, A. A. De Koeijer, and P. Reijders, The force of infection in populations of varying size: A modeling problem, Journal of Biological Systems 3 (1995), no. 2, 519-529.
13. Le Dung, Global attractors for a class of degenerate nonlinear parabolic systems, J. Diff. Eqns., 147 (1998), pp. 1-29.
14. W.E. Fitzgibbon and M. Langiais, Diffusive seir models with logistic population control, Communication on Applied Nonlinear Analysis 4 (1997), 1-16.
15. W.E. Fitzgibbon, M. Langiais, and J.J. Morgan, Eventually uniform bounds for a class of quasipositive reaction-diffusion systems, Japan Journal of Industrial And Applied Mathematics 16 (1999), no. 2, 225-241.
16. W.E. Fitzgibbon, J. J. Morgan, and S.J Waggoner, A quasilinear system modeling the spread of infectious disease, Rocky Mountain Journal of Mathematics 2 (1992), 579-592.
17. E. Fromont, M. Artois, M. Langlais, F. Courchamp, and D. Pontier, Modelling the feline leukemia virus (felv) in a natural population of cats (it Felis catus), Theoretical Population Biology 52 (1997), 60-70.
18. E. Fromont, D. Pontier, and M. Langlais, Dynamics of a feline retroviretrovirusrus (felv) in host populations with variable structures, (1998).
19. L. Hadjadj, T. Aliziane, and M. S. Moulay, Non linear reaction diffusion system of degenerate parabolic type (submitted).
20. M. C. De Jong, O. Diekmann, and H. Heesterbeek, How does transmission of infection depend on population size? epidemic models, Publication of the Newton Institute (1995), no. 5, 84-94.
21. W.O Kermack and A.G. McKendrick, Contribution to the mathematical theory of epidemics, ii-the problem of endemicity, Proc. Roy. Soc. Edin A 138 (1932), 55-83.
22. O.A. Ladyzenskaja, V.A. Solonikov, and N.N. Ural'ceva, Linear and quasilinear equation of parabolic type, Transl. Math. Monographs, vol. 23, American Math. Society, Providence, 1968.
23. M. Langlais and Ch. Suppo, A remark on a generic seirs model and application to cat retroviruses and fox rabies, Mathematical and Computer Modelling 31 (2000), 117-124.
24. L. Maddalena, Existence, uniqueness and qualitative properties of the solution of a degenerate nonlinear parabolic system, J. Math. Anal. Applications 127 (1987), 443-458.
25. O. A. Oleinik, A. S. Kalashnikov, and C. Yui-Lin, The cauhy problem and boundary value problem for the equation of insteady filtration type, Izv. Akad. Nauk SSSR, Soc. Math. 22 (1958), 667-704.
26. J. Smoller, Shock waves and reaction-diffusion equation, Springer, Berlin Heidelberg New York Tokyo, 1983.
27. G.F. Webb, Reaction diffusion model for deterministic diffusive epidemics, J. Math. App 84 (1981), 150-161.