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Traveling front solutions for a diffusive epidemic model with external sources
Smaïl Djebali
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, p. 271-292
@article{AFST_2001_6_10_2_271_0,
     author = {Djebali, Sma\"\i l},
     title = {Traveling front solutions for a diffusive epidemic model with external sources},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 6, 10},
     number = {2},
     year = {2001},
     pages = {271-292},
     mrnumber = {1896182},
     zbl = {0995.92040},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2001_6_10_2_271_0}
}
Djebali, Smaïl. Traveling front solutions for a diffusive epidemic model with external sources. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 10 (2001) no. 2, pp. 271-292. afst.centre-mersenne.org/item/AFST_2001_6_10_2_271_0/

[1] Aronson (D.G.) & Weinberger (H.F.). - Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. (1978), pp. 33-76. | Zbl 0407.92014

[2] Bailey (N.T.). - The Mathematical Theory of Infectious Diseases, Griffin, 1975. | MR 452809 | Zbl 0334.92024

[3] Berestycki (H.), Nicolaenko (B.) & Scheurer (B.). - Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal., Vol. 16, No 6 (1985), pp. 1207-1242. | Zbl 0596.76096

[4] Britton (N.F.). - Reaction-Diffusion Equations and their Applications to Biology, Academic Press, 1986. | MR 866143 | Zbl 0602.92001

[5] Mottoni (P. De), Orlandi (E.) & Tesei (A.). - Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection, Nonlinear Analysis. Theory, Methods and Applications. Vol. 3 (1979), pp. 663-675. | Zbl 0416.35009

[6] Djebali (S.). - Traveling wave solutions to a reaction-diffusion system arising in epidemiology, Nonlinear Analysis: Real World Applications, Vol. 2, No 4 (2001), pp. 417-442. | MR 1858897 | Zbl 1017.92029

[7] Fife (P.C.). - Mathematical Aspects of Reacting and Diffusing Systems, in Lecture Notes in Biomathematics, No 28, Springer Verlag, 1979. | MR 527914 | Zbl 0403.92004

[8] Hosono (Y.) & Ilyas (B.). - Traveling waves for a simple diffusive epidemic model, Math. Models and Meth. in Applied Sciences, Vol. 5, No 7 (1995), pp. 935-966. | Zbl 0836.92023

[9] Kermack (W.O.) & Mckendrick (A.G.). - Contributions to the mathematical theory of epidemics, Pro. Roy. Soc., A115 (1927), pp. 700-721. | JFM 53.0517.01

[10] Lloyd (N.G.). - Degree Theory, Cambridge University Press, 1978. | MR 493564 | Zbl 0367.47001

[11] Marion (M.). - Qualitative properties of a nonlinear system for laminar flames without ignition temperature, Nonlinear Analysis. Theory, Methods and Applications. Vol. 9, No 11 (1985), pp.1269-1292. | MR 813658 | Zbl 0648.76051

[12] Murray (J.D.). - Mathematical Biology, Springer Verlag, 1989. | MR 1007836 | Zbl 0682.92001

[13] Pao (C.V.). - On nonlinear reaction-diffusion systems, Journal of Mathematical Analysis and Applications, Vol. 87 (1982), pp. 165-198. | MR 653613 | Zbl 0488.35043

[14] Waltman (P.). - Deterministic Threshold Models in the Theory of Epidemics, Lecture Notes in Biomathematics, Vol. 1, Springer-Verlag, Berlin, New York, 1974. | MR 359874 | Zbl 0293.92015

[15] Uchiyama (K.). - The behaviour of some nonlinear diffusion equations for large time, J. Kyoto Univ., Vol. 18, (1978) pp. 453-508. | MR 509494 | Zbl 0408.35053