Traveling waves of the spread of avian influenza

Proceedings of the American Mathematical Society

Volumn 140, Issue 11, 2012, Pages 3931-3946

  Wang, Zhi Cheng ^a   Wu, Jianhong ^b   Liu, Rongsong ^c  

^a LANZHOU UNIVERSITY   (China)

^b YORK UNIVERSITY   (Canada)

^c UNIVERSITY OF WYOMING   (United States)

Author keywords

Avian influenza; Disease spread; Epidemic wave

Indexed keywords

EID: 84863922084     PISSN: 00029939     EISSN: 10886826     Source Type: Journal    
DOI: 10.1090/S0002-9939-2012-11246-8     Document Type: Article

References (10)

1. S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727. MR0125307 (23:A2610)
2. S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math. 17 (1964), 35-92. MR0162050 (28:5252)
3. A. Berman, M. Neumann, Ronald J. Stern, Nonnegative matrices in dynamic systems, John Wiley & Sons, New York, 1989. MR1019319 (90j:93030)
4. A. Ducrot, P. Magal, Travelling wave solutions for an infection-age structured model with diffusion, Proc. Royal Soc. Edinburgh (A) 139 (2009), 459-482. MR2506782 (2010f:35417)
5. A. Ducrot, P. Magal, S. Ruan, Travelling wave solutions in multigroup age-structured epidemi models, Arch. Rational Mech. Anal. 195 (2010), 311-331. MR2564476
6. D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order, Springer, Berlin, 2001. MR1814364 (2001k:35004)
7. M. Hirsch, H. Hanish, J.-P. Gabriel, Differential equation model of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math. 38 (1985), 733-753. MR812345 (87f:92015)
8. Y. Hosono, B. Ilyas, Traveling waves for a simple diffusive epidemic model, Math. Models Methods Appl. Sci. 5 (1995), 935-966. MR1359215 (96j:35248)
9. R. Liu, V.R.S.K. Duvvuri, J. Wu, Spread pattern formation of H5N1-avian influenza and its implications for control strategies, Math. Model. Nat. Phenom. 3(7) (2008), 161-179. MR2460260 (2009j:92059)
10. Z.C. Wang, J. Wu, Traveling waves of a diffusive Kermack-McKendrick epidemic model with non-local delayed transmission, Proc. R. Soc. London Ser. A 466 (2010), 237-261. MR2564926 (2011b:92072)