Some vector borne diseases with structured host populations: Extinction and spatial spread

SIAM Journal on Applied Mathematics

Volumn 67, Issue 2, 2006, Pages 408-433

  Gourley, Stephen A ^a   Liu, Rongsong ^b   Wu, Jianhong ^c  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b PURDUE UNIVERSITY   (United States)

^c YORK UNIVERSITY   (Canada)

Author keywords

Delay; Epidemic; Stage structure; Traveling front; Vector borne disease

Indexed keywords

DELAY DIFFERENTIAL EQUATIONS; DISEASE ERADICATION; TRAVELING FRONT; VECTOR BORNE DISEASES;

DIFFERENTIAL EQUATIONS; DISEASES; EPIDEMIOLOGY; MATHEMATICAL MODELS;

POPULATION DYNAMICS;

EID: 34247587066     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050648717     Document Type: Article

References (28)

1. R. M. ANDERSON AND R. M. MAY, Infectious Diseases of Humans, Oxford University Press, London, 1991.
2. J. S. BLACKMORE AND R. P. DOW, Differential feeding of Culex tarsalis on nestling and adult birds, Mosq. News, 18 (1958), pp. 15-17.
3. C. BOWMAN, A. B. GUMEL, P. VAN DEN DRIESSCHE, J. WU, AND H. ZHU, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 67 (2005), pp. 1107-1133.
4. F. BRAUER AND C. CASTILLO-CHAVEZ, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
5. O. DIEKMANN AND J. A. P. HEESTERBEEK, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley Ser. Math. Comput. Biol., John Wiley and Sons, Chichester, UK, 2000.
6. L. EDELSTEIN-KESHET, Mathematical Models in Biology, Birkhäuser Math. Ser., McGraw-Hill, Toronto, 1988.
7. S. A. GOURLEY, J. W.-H. SO, AND J. WU, Nonlocal reaction-diffusion equations with delay: Biological models and nonlinear dynamics, J. Math. Sci., 124 (2004), pp. 5119-5153.
8. S. A. GOURLEY AND J. Wu, Delayed non-local diffusive systems in biological invasion and disease spread, in Nonlinear Dynamics and Evolution Equations, Fields Inst. Commun. 48, Amer. Math. Soc., Providence, RI, 2006, pp. 137-200.
9. W. S. C. GURNEY, S. P. BLYTHE, AND R. M. NISBET, Nicholson's blowflies revisited, Nature, 287 (1980), pp. 17-21.
10. H. W. HETHCOTE, The mathematics of infectious diseases, SIAM Rev., 42 (2000), pp. 599-653.
11. Y. HOSONO, The minimal speed of traveling fronts for a diffusive Lotka Volterra competition model, Bull. Math. Biol., 60 (1998), pp. 435-448.
12. D. S. JONES AND B. D. SLEEMAN, Differential Equations and Mathematical Biology, Chapman & Hall/CRC Math. Biol. Med. Ser., Chapman & Hall/CRC, Boca Raton, FL, 2003.
13. M. KOT, Elements of Mathematical Ecology, Cambridge University Press, Cambridge, UK, 2001.
14. Y. KUANG, Delay Differential Equations with Applications in Population Dynamics, Math. Sci. Engrg. 191, Academic Press, Boston, MA, 1993.
15. M. A. LEWIS, B. LI, AND H. F. WEINBERGER, Spreading speed and linear determinancy for two-species competition models, J. Math. Biol., 45 (2002), pp. 219-233.
16. M. LEWIS, J. RENCLAWOWICZ, AND P. VAN DEN DRIESSCHE, Traveling waves and spread rates for a West Nile virus model, Bull. Math. Biol., 68 (2006), pp. 3-23.
17. X. LIANG AND X.-Q. ZHAO, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), pp. 1-40.
18. C. C. LORD AND J.F. DAY, Simulation studies of St. Louis encephalitis virus in south Florida Vector Borne and Zoonotic Diseases, 1 (2001), pp. 299-315.
19. C. C. LORD AND J.F. DAY, Simulation studies of St. Louis encephalitis and West Nile viruses: The impact of bird mortality, Vector Borne and Zoonotic Diseases, 1 (2001), pp. 317-329.
20. J. D. MURRAY, Mathematical Biology, Springer-Verlag, New York, 1993.
21. A. OKUBO, Diffusion-type models for avion range expansion, in Proceedings of the 19th International Ornithological Congress (Ottawa), Vol. l, H. Queslet, ed., 1988, pp. 1038-1049.
22. T. W. SCOTT, L. H. LORENZ, AND J. D. EDMAN, Effects of house sparrow age and arbovirus infection on attraction of mosquitoes, J. Med. Entomol., 27 (1990), pp. 856-863.
23. H. L. SMITH, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Amer. Math. Soc., Providence, RI, 1995.
24. H. R. THIEME AND X.-Q. ZHAO, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, J. Differential Equations, 195 (2003), pp. 430-470.
25. H. F. WEINBERGER, M. A. LEWIS, AND B. LI, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), pp. 183-218.
26. M. J. WONHAM, T. DE-CAMINO-BECK, AND M. A. LEWIS, An epidemiological model for West Nile virus: Invasion analysis and control applications, Proc. R. Soc. London Ser. B, 271 (2004), pp. 501-507.
27. M. J. WONHAM, M. A. LEWIS, J. RENCLAWOWICZ, AND P. VAN DEN DRIESSCHE, Transmission assumptions generate conflicting predictions in host-vector disease models: A case study in West Nile virus, Ecol. Lett., 9 (2006), pp. 706-725.
28. J. WU, Global dynamics of strongly monotone retarded equations with infinite delay, J. Integral Equations Appl., 4 (1992), pp. 273-307.