Invasion dynamics of epidemic with the Allee effect

BioSystems

Volumn 105, Issue 1, 2011, Pages 25-33

  Wang, Wenting ^a,b   Liu, Hua ^a   Li, Zizhen ^b   Guo, Zhongkai ^c   Yang, Yuhua ^b  

^a NORTH MINZU UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

^c LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Allee effect; Biological invasion; Eco epidemiology; Invasion speed; Partial differential equations

Indexed keywords

ALLEE EFFECT; BIOLOGICAL INVASION; CATASTROPHE THEORY; CHAOTIC DYNAMICS; DIFFUSION; EPIDEMIC; EPIDEMIOLOGY; LIMIT ANALYSIS; NONLINEARITY; NUMERICAL MODEL; PREDATOR-PREY INTERACTION;

ARTICLE; EPIDEMIC; HUMAN; INFECTION RATE; NONHUMAN; POPULATION ABUNDANCE; POPULATION DENSITY; POPULATION GROWTH; PREDATOR PREY INTERACTION; SIMULATION; SPECIES EXTINCTION; SPECIES INVASION;

EID: 79957800811     PISSN: 03032647     EISSN: 18728324     Source Type: Journal    
DOI: 10.1016/j.biosystems.2011.03.001     Document Type: Article

References (50)

1. Allee W.C. Animal Aggregations, A Study in General Sociology 1931, University of Chicago Press, Chicago.
2. Allee W.C. The Social Life of Animals 1938, Norton and Co., New York.
3. Amarasekare P. Interactions between local dynamics and dispersal: insights from single species models. Theor. Popul. Biol. 1998, 53:44-59.
4. Amarasekare P. Spatial dynamics of mutualistic interactions. J. Anim. Ecol. 2004, 73:128-140.
5. Amarasekare P. Productivity, dispersal and the coexistence of intraguild predators and prey. J. Theor. Biol. 2006, 243:121-133.
6. Anderson R.M., May R.M. The invasion, persistence, and spread of infectious diseases within animal and plant communities. Philos. Trans. R. Soc. Lond. B 1986, 314:533-570.
7. Andow D.A., Kareiva P.M., Levin S.A., Okubo A. Spread of invading organisms. Landscape Ecol. 1990, 4:177-188.
8. Barbour A., Mollison D. Epidemics and Random Graphs. Stochastic Processes in Epidemic Theory 1990, Springer, New York.
9. Berryman A.A. Population Systems: A General Introduction 1981, Plenum Press, New York.
10. Chen L.L., Hui C. Habitat destruction and the extinction debt revisited: the Allee effect. Math. Biosci. 2009, 221:26-32.
11. Courchamp F., Clutton-Brock T., Grenfell B. Inverse density dependence and the Allee effect. TREE 1999, 14:405-410.
12. Courchamp F., Grenfell B., Clutton-Brock T. Population dynamics of obligate cooperators. Proc. R. Soc. Lond. Ser. B: Biol. Sci. 1999, 266:557-563.
13. Çelik C., Duman O. Allee effect in a discrete-time predator-prey system. Chaos Solitons Fractals 2009, 40:1956-1962.
14. Dennis B. Allee effects: population growth, critical density, and the chance of extinction. Nat. Res. Model. 1989, 3:481-538.
15. Fisher R. The wave of advance of advantageous genes. Ann. Eugenics 1937, 7:255-369.
16. Fowler M.S., Ruxton G.D. Population dynamic consequences of Allee effects. J. Theor. Biol. 2002, 215:39-46.
17. Frantzen J., van den Bosch F. Spread of organisms: can travelling and dispersive waves be distinguished?. Basic Appl. Ecol. 2000, 1:83-91.
18. Gulland F.M.D. The impact of infectious diseases on wild animal populations-a review. Ecology of Infectious Diseases in Natural Populations 1995, Cambridge University Press, Cambridge.
19. Gyllenberg M., Hemminki J., Tammaru T. Allee effects can both conserve and create spatial heterogeneity in population densities. Theor. Popul. Biol. 1999, 56:231-242.
20. Hastings A. Models of spatial spread: a synthesis. Biol. Conserv. 1996, 78:143-148.
21. Hengeveld R. Dynamics of Biological Invasions 1989, Chapman and Hall, London.
22. Hethcote H.W., Wang W.D., Han L.T., Ma Z.E. A predator-prey model with infected prey. Theor. Popul. Biol. 2004, 66:259-268.
23. Holt R.D., Polis G.A. A theoretical framework for interguild predation. Am. Nat. 1997, 149:745-764.
24. Holmes E.E., Lewis M.A., Banks J.E., Veit R.R. Partial differential equations in ecology: spatial interactions and population dynamics. Ecology 1994, 75:17-29.
25. Johansen A. Spatio-temporal self-organisation in a model of disease spreading. Physica D 1994, 78:186-193.
26. Keeling M.J. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. 1999, 266:859-867.
27. Keitt T.H., Lewis M.A., Holt R.D. Allee effects, invasion pinning, and species borders. Am. Nat. 2001, 157:203-216.
28. Kermack W.O., McKendrick A.G. Contributions to the mathematical theory of epidemics, part I. Proc. R. Soc. A 1927, 115:700-721.
29. Kermack W.O., McKendrick A.G. Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proc. R. Soc. A 1932, 138:55-83.
30. Kuussaari M., Saccheri I., Camara M., Hanski I. Allee effect and population dynamics in the Glanville fritillary butterfly. Oikos 1998, 82:384-392.
31. Lewis M.A., Kareiva P. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 1993, 43:141-158.
32. Malchow H. Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics. Proc. R. Soc. Lond. B 1993, 251:103-109.
33. McCarthy M.A. The Allee effect, finding mates and theoretical models. Ecol. Model. 1997, 103:99-102.
34. Morozov A., Petrovskii S., Li B.L. Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect. J. Theor. Biol. 2006, 238:18-35.
35. Murray J.D. Mathematical Biology 1993, Springer-Verlag, New York.
36. Mylius S.D., Klumpers K., de Roos A.M., Persson L. Impact of intraguild predation and stage structure on simple communities along a productivity gradient. Am. Nat. 2001, 158:259-276.
37. Nentwig W. Biological Invasion 2007, Springer-Verlag, Berlin/Heidelberg.
38. Okubo A. Diffusion and Ecological Problems: Mathematical Models 1980, Springer, Berlin.
39. Owen M.R., Lewis M.A. How predation can slow, stop or reverse a prey invasion. Bull. Math. Biol. 2001, 63:655-684.
40. Petrovskii S.V., Morozov A.Y., Li B.L. Regimes of biological invasion in a predator-prey system with the Allee effect. Bull. Math. Biol. 2005, 67:637-661.
41. Reinhardt K., Köhler G. Conservation of the red-winged grasshopper. Oedipoda germanica (Latr.): the influence of reproductive behaviour. Biol. Conserv. 2002, 107:221-228.
42. Sherratt J.A. Periodic travelling waves in cyclic predator-prey systems. Ecol. Lett. 2001, 4:30-37.
43. Shigesada N., Kawasaki K. Biological Invasions: Theory and Practice 1997, Oxford University Press, Oxford.
44. Scheuring I. Allee effect increases the dynamical stability of populations. J. Theor. Biol. 1999, 199:407-414.
45. Skellam J.G. Random dispersal in theoretical populations. Biometrika 1951, 38:196-218.
46. Su M., Hui C., Zhangc Y., Li Z. Spatiotemporal dynamics of the epidemic transmission in a predator-prey system. Bull. Math. Biol. 2008, 70:2195-2210.
47. Venturino E. Epidemics in predator-prey models: disease in the predators. J. Math. Appl. Med. Biol. 2002, 19:185-205.
48. Wang M.H., Kot M. Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 2001, 171:83-97.
49. Wang G., Liang X., Wang F. The competitive dynamics of populations subject to an Allee effect. Ecol. Model. 1999, 124:183-192.
50. Zhou S.R., Liu Y.F., Wang G. The stability of predator-prey systems subject to the Allee effects. Theor. Popul. Biol. 2005, 67:23-31.