Traveling waves and spread rates for a west nile virus model

Bulletin of Mathematical Biology

Volumn 68, Issue 1, 2006, Pages 3-23

  Lewis, Mark ^a   Rencławowicz, Joanna ^a,b,c   Van Den Driessche, P ^c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b INSTITUTE OF MATHEMATICS   (Poland)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Comparison theorems; Spread rate; Traveling waves; West Nile virus model

Indexed keywords

AVES; WEST NILE VIRUS;

ALGORITHM; ANIMAL; ANIMAL DISEASE; ARTICLE; BIOLOGICAL MODEL; BIRD; DISEASE TRANSMISSION; HUMAN; MOSQUITO; NORTH AMERICA; PHYSIOLOGY; POPULATION MIGRATION; VIROLOGY; VIRUS INFECTION; WEST NILE FLAVIVIRUS;

ALGORITHMS; ANIMAL MIGRATION; ANIMALS; BIRDS; CULICIDAE; HUMANS; MODELS, BIOLOGICAL; NORTH AMERICA; WEST NILE FEVER; WEST NILE VIRUS;

EID: 33646853385     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-005-9018-z     Document Type: Article

References (13)

1. Hadeler, K., Lewis, M., 2002. Spatial dynamics of the diffusive logistic equation with a sedentary compartment. CAMQ 10, 473-499.
2. Komar, N., Langevin, S., Hinten, S., Nemeth, N., Edwards, E., Hettler, D., Davis, B., Bowen, R., Bunning, M., 2003. Experimental Infection of North American birds with the New York 1999 strain of West Nile virus. Emerg. Inform. Dis. 9(3), 311-322.
3. Lewis, M., Li, B., Weinberger, H., 2002. Spreading speed and linear determinacy for two species competition models. J. Math. Biol. 45, 219-233.
4. Li, B., Weinberger, H., Lewis, M., 2005. Spreading speeds as slowest wave speeds for cooperative systems. Math. Biosci.196, 82-98.
5. Lu, G., Sleeman, B.D., 1993. Maximum principles and comparison theorems for semilinear parabolic systems and their applications. Proc. R. Soc. Edinburgh A 123, 857-885.
6. Lui, R., 1989a. Biological growth and spread modeled by system of recursions. I. Math. Theor. Math. Biosci. 93, 269-295.
7. Lui, R., 1989b. Biological growth and spread modeled by system of recursions. II. Biological theory. Math. Biosci. 93, 297-312.
8. Okubo, A., 1998. Diffusion-type models for avian range expansion. In: Henri Quellet, I. (Ed.), Acta XIX Congressus Internationalis Ornithologici. National Museum of Natural Sciences, University of Ottawa Press, pp. 1038-1049.
9. Smoller, J., 1983. Shock Waves and Reaction-Diffusion Systems. Springer-Verlag, New York.
10. van den Driessche, P., Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29-48.
11. Volpert, A.I., Volpert, V.A., Volpert, V.A., 1994. TravelingWave Solutions of Parabolic Systems, Vol. 140. American Mathematical Society, Providence, RI.
12. Weinberger, H., Lewis, M., Li, B., 2002. Analysis of linear determinacy for spread in cooperative models. J. Math. Biol. 45, 183-218.
13. Wonham, M.J., de Camino-Beck, T., Lewis, M., 2004. An epidemiological model for West-Nile virus: Invasion analysis and control application. Proc. R. Soc. Lond. B 271, 501-507.