Modeling the circulation of a disease between two host populations on non coincident spatial domains

Biological Invasions

Volumn 7, Issue 5, 2005, Pages 863-875

  Fitzgibbon, W E ^a   Langlais, M ^b   Marpeau, F ^b   Morgan, J J ^c  

^a UNIVERSITY OF HOUSTON   (United States)

^b UNIVERSITÉ BORDEAUX 1   (France)

^c University of Houston   (United States)

Author keywords

Distinct spatial domains; Large time behavior; Reaction diffusion equations

Indexed keywords

DISEASE SPREAD; MODELING; UNGULATE;

ODOCOILEUS VIRGINIANUS;

EID: 23944520383     PISSN: 13873547     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10530-005-5210-1     Document Type: Conference Paper

References (28)

1. NTJ Bailey 1975 The Mathematical Theory of Infectious Diseases and its Applications 2 Hafner Press New York 413
2. S Busenberg KC Cooke 1993 Vertically transmitted diseases, Biomathematics Volume 23 Springer Verlag New York 248
3. RS Cantrell C Cosner 2003 Spatial Ecology Via Reaction Equations John Wiley and Sons Chichester, UK 456
4. O Diekmann MCM De Jong AA De Koeijer P Reijnders 1995 The force of infection in populations of varying size: a modeling problem Journal of Biological Systems 3 519 529
5. WE Fitzgibbon M Langlais 1997 Diffusive SEIR models with logistic population control Communications on Applied Nonlinear Analysis 4 1 16
6. WE Fitzgibbon JJ Morgan R Sanders 1992 Global existence and boundedness for a class of inhomogeneous semilinear parabolic equations Nonlinear Analysis TMA 19 885 899
7. WE Fitzgibbon C Martin JJ Morgan 1994 Uniform bounds and asymptotic behavior for a diffusive epidemic model with criss-cross dynamics Journal of Mathematical Analysis and Applications 184 399 414
8. WE Fitzgibbon M Langlais ME Parrott GW Webb 1995 A diffusive system with age dependence modeling FIV Nonlinear Analysis TMA 25 975 989
9. WE Fitzgibbon M Parrott GF Webb 1995 Diffusive epidemic models with criss-cross dynamics Mathematical Biosciences 128 131 155
10. WE Fitzgibbon M Langlais JJ Morgan 1999 Eventually uniform bounds for a quasipositive reaction diffusion system Japan Journal of Industrial and Applied Mathematics 16 225 241
11. WE Fitzgibbon M Langlais JJ Morgan 2001 A mathematical model of the spread of feline leukemia virus (FeLV) through a highly heterogeneous domain SIAM Journal of Mathematical Analysis 33 570 588
12. WE Fitzgibbon M Langlais JJ Morgan 2004 A reaction-diffusion system modeling direct and indirect transmission of a disease DCDS B 4 893 910
13. WE Fitzgibbon M Langlais JJ Morgan 2004 A reaction diffusion system on non-coincident domains modeling the circulation of a disease between two host Populations Differential and Integral Equations 17 781 802
14. J Hale 1988 Asymptotic Behavior of Dissipative Systems American Mathematical Society Providence, Rhode Island 198
15. D Henry 1981 Geometric Theory of Semilinear Parabolic Equations Springer-Verlag Berlin 348
16. S Hollis RH Martin M Pierre 1987 Global existence and boundedness in reaction diffusion systems SIAM Journal of Mathematical Analysis 18 744 761
17. OA Ladyzenskaja V Solonnikov N Ural'ceva 1968 Linear and quasilinear equations of parabolic type Translations of AMS 23 Providence, Rhode Island 736
18. JJ Morgan 1989 Global existence for semilinear parabolic systems SIAM Journal of Mathematical Analysis 20 1128 1144
19. JJ Morgan 1990 Boundedness and decay results for reaction diffusion systems SIAM Journal of Mathematical Analysis 21 1172 1184
20. GE Olsson N White C Ahlm F Elgh A-C Verlemyr P Juto 2002 Demographic factors associated with hantavirus infection in bank voles (Clethrionomys glareolus) Emerging Infectious Diseases 8 924 929
21. A Pazy 1983 Semigroups of Linear Operators and Applications to Partial Differential Equations Springer Verlag Berlin 279
22. F Sauvage C Penalba P Vuillaume F Boue D Coudrier D Pontier 2002 Puumala hantavirus infection in humans and in the reservoir host, Ardennes region, France Emerging Infectious Diseases 8 1509 1511
23. F Sauvage M Langlais NG Yoccoz D. Pontier 2003 Modelling hantavirus in cyclic bank voles the role of indirect transmission on virus persistence Journal of Animal Ecology 72 1 13
24. C Schmaljohn B Hjelle 1997 Hantaviruses: a global disease problem Emerging Infectious Diseases 3 2 95 104
25. OJ Schmitz TD Nudds 1994 Parasite-mediated competition in deer and moose: how strong is the effect of meningeal worm on moose? Ecological Applications 4 91 103
26. G Sell Y You 2002 Dynamics of Evolutionary Systems Springer-Verlag New York 670
27. J Shaman JF Day M Stieglitz 2002 Drought-induced amplification of Saint Louis encephalitis virus Florida. Emerging Infectious Diseases 8 575 580
28. J Smoller 1983 Shock Waves and Reaction Diffusion Equations Springer Verlag New York 632