Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations

Journal fur die Reine und Angewandte Mathematik

Volumn 1979, Issue 306, 1979, Pages 94-121

  Thieme, Horst R ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008260279     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1979.306.94     Document Type: Article

References (19)

1. D. G. Aronson, The asymptotic speed of propagation of a simple epidemic, in W. E. Fitzgibbon, H. F. Walker (ed.), Nonlinear Diffusion, Research Notes in Mathematics 14 (1977), 1–23.
2. D. G. Aronson, Topics in Nonlinear Diffusion, Regional Conference Series in Applied Mathematics, CBMS/NSF, SIAM, Philadelphia, to appear.
3. D. G. Aronson, H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in J. Goldstein (ed.), Partial Differential Equations and Related Topics, Lecture Notes in Math. 446, Berlin-Heidelberg-New York 1975.
4. D. G. Aronson, H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., to appear.
5. C. Atkinson, G. E. H. Reuter, Deterministic epidemic waves, Math. Proc. Cambr. Phil. Soc. 80 (1976), 315–330.
6. L. R. Clark, P. W. Geier, R. D. Hughes, R. F. Morris, The Ecology of Insect Populations in Theory and Practice, London 1967.
7. O. Diekmann, Thresholds and travelling waves for the geographical spread of infection, J. Math. Biology, to appear.
8. N. Dunford, J. T. Schwartz, Linear Operators. I, New York 1957.
9. S. Hein, Zur Epidemiologie der Wildtollwut, Statistische Analysen des Seuchenzuges im Odenwald in der Zeit vom Januar 1973 bis Mai 1976, thesis (1976), Mainz.
10. F. Hoppensteadt, Mathematical Theories of Populations: Demographics, Genetics and Epidemics, Regional Conference Series in Applied Mathematics 20 (1975), CBMS/NCF, SIAM, Philadelphia.
11. D. G. Kendall, in discussion on M. S. Bartlett, Measles periodicity and community size, J. R. statist. Soc. Ser. A120 (1957), 48–70.
12. D. G. Kendall, Mathematical models of the spread of infection, Mathematics and Computer Science in Biology and Medicine (1965), 213–225.
13. W. D. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. A115 (1927), 700.
14. H. Mogel, F. Knorpp, K. Bögel, A. A. Arata, K. Dietz und P. Diethelm, Zur Epidemiologie der Wildtier-tollwut, Untersuchungen im siidlichen Teil der Bundesrepublik Deutschland, Zbl. Vet. Med. B21 (1974), 647–659.
15. F. Schwerdtfeger, Ökologie der Tiere. II: Demökologie, Hamburg-Berlin 1968.
16. H. R. Thieme, A model for the spatial spread of an epidemic, J. Math. Biology 4 (1977), 337–351.
17. F. J. Vernberg, W. B. Vernberg, The Animal and the Environment, New York-Chicago-San Francisco-Atlanta-Dallas-Montreal-Toronto-London-Sydney 1970.
18. Paul Waltman, Deterministic Threshold Models in the Theory of Epidemics, Lecture Notes in Biomathematics 1, Berlin-Heidelberg-New York 1974.
19. H. F. Weinberger, Asymptotic behavior of a model in population genetics, in J. Chadam (ed.), Nonlinear Partial Differential Equations and Applications, Lecture Notes in Math. 648, Berlin-Heidelberg-New York 1978.