Spatial patterns in a discrete-time SIS patch model

Journal of Mathematical Biology

Volumn 58, Issue 3, 2009, Pages 339-375

  Allen, L J S ^a   Lou, Y ^b   Nevai, A L ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Basic reproduction number; Disease free equilibrium; Dispersal; Endemic equilibrium; Habitat connectivity; Spatial heterogeneity

Indexed keywords

ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; ECOSYSTEM; HUMAN; IMMUNOLOGY;

BASIC REPRODUCTION NUMBER; COMMUNICABLE DISEASES; ECOSYSTEM; HUMANS; MODELS, BIOLOGICAL;

EID: 58149276997     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0194-y     Document Type: Article

References (32)

1. L.J.S. Allen B.M. Bolker Y. Lou A.L. Nevai 2007 Asymptotic profile of the steady states for an SIS epidemic patch model SIAM J. Appl. Math. 67 1283 1309
2. L.J.S. Allen B.M. Bolker Y. Lou A.L. Nevai 2008 Asymptotic profile of the steady states for an SIS epidemic reaction-diffusion model Discr. Cont. Dyn. Sys. A. 21 1 20
3. L.J.S. Allen A. Burgin 2000 Comparison of deterministic and stochastic SIS and SIR models in discrete time Math. Biosci. 163 1 33
4. L.J.S. Allen M.A. Jones C.F. Martin 1991 A discrete-time model with vaccination for a measles epidemic Math. Biosci. 105 111 131
5. L.J.S. Allen N. Kirupaharan S.M. Wilson 2004 SIS epidemic models with multiple pathogen strains J. Differ. Equ. Appl. 10 53 75
6. Allen, L.J.S., van den Driessche, P.: The basic reproduction number in some discrete-time epidemic models. J. Differ. Equ. Appl. (2008) (in press)
7. J. Arino R. Jordan P. van den Driessche 2007 Quarantine in a multi-species epidemic model with spatial dynamics Math. Biosci. 206 46 60
8. T. Caraco M. Duryea G. Gardner W. Maniatty B.K. Szymanski 1998 Host spatial heterogeneity and extinction of an SIS epidemic J. Theor. Biol. 192 351 361
9. C. Carrillo P. Fife 2005 Spatial effects in discrete generation population models J. Math. Biol. 50 161 188
10. C. Castillo-Chavez A.-A. Yakubu 2001 Dispersal, disease and life-history evolution Math. Biosci. 173 35 53
11. Castillo-Chavez C., Yakubu A.-A.: Intraspecific competition, dispersal, and disease dynamics in discrete-time patchy environments. In: Castillo-Chavez, C., Blower, S., Driessche, P., Kirschner, D., Yakubu, A.-A. (eds) Mathematical Approaches for Emerging and Reemerging Infectious Diseases An Introduction, pp. 165-181. Springer, New York (2002)
12. Cushing, J.M.: An Introduction to Structured Population Dynamics. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, PA (1998)
13. J.M. Cushing Z. Yicang 1994 The net reproductive value and stability in structured population models Nat. Resour. Model. 8 1 37
14. 0 for discrete-time epidemic models with dynamic heterogeneity Math. Biosci. 119 97 114
15. T. Dhirasakdanon H. Thieme P. van den Driessche 2007 A sharp threshold for disease persistence in host metapopulations J. Biol. Dyn. 1 363 378
16. Diekmann O., Heesterbeek J.A.P.: Mathematical Epidemiology of Infectious Diseases. Wiley, Chichester (2000)
17. O. Diekmann J.A.P. Heesterbeek J.A.J. Metz 1990 On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations J. Math. Biol. 28 365 382
18. M. Doebeli G.D. Ruxton 1998 Stabilization through pattern formation in metapopulations with long-range dispersal Proc. R. Soc. Lond. B. 265 1325 1332
19. K.E. Emmert L.J.S. Allen 2004 Population persistence and extinction in a discrete-time, stage-structured epidemic model J. Differ. Equ. Appl. 10 1177 1199
20. Gantmacher F.R.: The Theory of Matrices, vol. II. Chelsea, New York (1960)
21. Y.-H. Hsieh P. van den Driessche L. Wang 2007 Impact of travel between patches for spatial spread of disease Bull. Math. Biol. 69 1355 1375
22. M.A. Lewis J. Rencławowicz P. van den Driessche 2006 Traveling waves and spread rates for a West Nile virus model Bull. Math. Biol. 68 3 23
23. M.A. Lewis J. Rencławowicz P. van den Driessche M. Wonham 2006 A comparison of continuous and discrete-time West Nile Virus models Bull. Math. Biol. 68 491 509
24. C.-K. Li H. Schneider 2002 Applications of Perron-Frobenius theory to population dynamics J. Math. Biol. 44 450 462
25. J. Medlock M. Kot 2003 Spreading disease: integro-differential equations old and new Math. Biosci. 184 201 222
26. Ortega J.M.: Matrix Theory: A Second Course. Plenum Press, New York (1987)
27. E.B. Postnikov I.M. Sokolov 2007 Continuum description of a contact infection spread in a SIR model Math. Biosci. 208 205 215
28. Ruan S.: Spatial-temporal dynamics in nonlocal epidemiological models. In: Takeuchi, Y., Sato, K., Iwasa, Y. (eds) Mathematics for Life Science and Medicine, vol 2, pp. 97-122. Springer, New York (2007)
29. Smith, H.: Monotone Dynamical Systems, An introduction to the theory of competitive and cooperative systems. American Mathematical Society, Mathematical Surveys and Monographs (1995)
30. P. van den Driessche J. Watmough 2002 Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 180 29 48
31. M.-H. Wang M. Kot M.G. Neubert 2002 Integrodifference equations, Allee effects, and invasions J. Math. Biol. 44 150 168
32. A.-A. Yakubu C. Castillo-Chavez 2002 Interplay between local dynamics and dispersal in discrete-time metapopulation models J. Theor. Biol. 218 273 288