Erratum: The asymptotic speed of spread and traveling waves for a vector disease model (Journal of Dynamics and Differential Equations (2006) 18 (1001-1019) (10.1007/s10884-006-9044-z));The asymptotic speed of spread and traveling waves for a vector disease model

Journal of Dynamics and Differential Equations

Volumn 18, Issue 4, 2006, Pages 1001-1019

  Zhao, Xiao Qiang ^a   Xiao, Dongmei ^b  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Comparison and iteration methods; Spreading speed; Traveling waves; Vector disease model

Indexed keywords

EID: 33750033198     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-007-9086-x     Document Type: Erratum

References (22)

1. Aronson, D. G., and Weinberger, H. F. (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In Goldstein, J. A. (ed.), Partial Differential Equations and Related Topics Lecture Notes in Mathematics, Vol. 446, Springer-Verlag, Berlin, pp. 5-49.
2. Brown, K. J., and Carr, J. (1977). Deterministic epidemic waves of critical velocity. Math. Proc. Camb. Philos. Soc. 81, 431-433.
3. Busenberg, S., and Cooke, K. L. (1978). Periodic solutions for a vector disease model. SIAM J. Appl. Math. 35, 704-721.
4. Cooke, K. L. (1979). Stability analysis for a vector disease model. Rocky Mt. J. Math. 9, 31-42.
5. Diekmann, O. (1978). Thresholds and traveling waves for the geographical spread of infection. J. Math. Biol. 6, 109-130.
6. Diekmann, O. (1979). Run for your life, A note on the asymptotic speed of propagation of an epidemic. J. Diff. Eq. 33, 58-73.
7. Liang, X., and Zhao, X.-Q. Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Commun. Pure Appl. Math., in press.
8. Lui, R. (1989). Biological growth and spread modeled by systems of recursions. I. Mathematical theory. Math. Biosci. 93, 269-295.
9. Ma, S. (2001). Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. J. Diff. Eq. 171, 294-314.
10. Marcati, P., and Pozio, M. A. (1980). Global asymptotic stability for a vector disease model with spatial spread. J. Math. Biol. 9, 179-187.
11. Martin, R. H., and Smith, H. L. (1990). Abstract functional differential equations and reaction-diffusion systems. Trans. Am. Math. Soc. 321, 1-44.
12. Murray, J. D. (2002). Mathematical Biology, I & II, Springer-Verlag, New York.
13. Rass, L., and Radcliffe, J. (2003). Spatial Deterministic Epidemics, Math. Surveys Monogr, Vol. 102, American Mathematical Society Providence, RI.
14. Ruan, S., and Xiao, D. (2004). Stability of steady states and existence of traveling waves in a vector disease model. Proc. R. Soc. Edinburgh 134A, 991-1011.
15. Smith, H. L. (1995). Monotone Dynamical Systems; An Introduction to the Theory of Competitive and Cooperative Systems, Math Surveys and Monographs 41, American Mathematical Society, Providence, RI.
16. Thieme, H. R. (1979). Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. J. Reine Angew. Math. 306, 94-121.
17. Thieme, H. R. (1979). Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. J. Math. Biol. 8, 173-187.
18. Thieme, H. R., and Zhao, X.-Q. (2003). Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models. J. Diff. Eq. 195, 430-470.
19. Volz, R. (1982). Global asymptotic stability of a periodic solution to an epidemic model. J. Math. Biol 15, 319-338.
20. Weinberger, H. F. (1982). Long-time behavior of a class of biological models. SIAM J. Math. Anal. 13, 353-396.
21. Wu, J., and Zou, X. (2001). Traveling wave fronts of reaction-diffusion systems with delay. J. Dyn. Diff. Eq. 13, 651-687.
22. Zhao, X.-Q., and Wang, W (2004). Fisher waves in an epidemic model. Discret. Contin. Dyn. Syst. Ser. B 4, 1117-1128.