Species decline and extinction: Synergy of infectious disease and allee effect?

Journal of Biological Dynamics

Volumn 3, Issue 2-3, 2009, Pages 305-323

  Thieme, Horst R ^a   Dhirasakdanon, Thanate ^a   Han, Zhun ^a   Trevino, Roy ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Amphibian disappearance; Chytridiomycosis; Epidemic; Global climate change; Incidence; Novel versus endemic pathogen hypothesis

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; EPIDEMIC; HOST PARASITE INTERACTION; HUMAN; INCIDENCE; PARASITOLOGY; POPULATION DYNAMICS; SPECIES DIFFERENCE; SPECIES EXTINCTION;

COMMUNICABLE DISEASES; EPIDEMICS; EXTINCTION, BIOLOGICAL; HOST-PARASITE INTERACTIONS; HUMANS; INCIDENCE; MODELS, BIOLOGICAL; POPULATION DYNAMICS; SPECIES SPECIFICITY;

EID: 77954654100     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513750802376313     Document Type: Article

References (45)

1. Allee, W. C., 1931. Animal Aggregations. A Study in General Sociology, Chicago:University of Chicago Press.
2. Allen, L. J.S., and van den Driessche, P., in press. The basic reproduction number in some discrete-time epidemic models. J. Differ. Eqn Appl.
3. Anderson, R. M., and May, R. M., 1979. Population biology of infectious diseases:Part I. Nature, 280:361–367.
4. Bazykin, A. D., 1998. Nonlinear Dynamics of Interacting Populations, Singapore:World Scientific.
5. Bazykin, A. D., and Berezovskaya, F. S., 1979. Allee effect, lower critical population density and dynamics of predator–prey system, Problemy ekologicheskogo monitoringa i modelirovaniya ecosistems 2, 161–175. Leningrad:Gidrometeoizdat.
6. Boyce, W. E., and DiPrima, R. C., 1992. Elementary Differential Equations and Boundary Value Problems, 5, New York:Wiley.
7. Brauer, F., and Nohel, J. A., 1989. The Qualitative Theory of Ordinary Differential Equations. An Introduction, New York:Dover.
8. Busenberg, S., and van den Driessche, P., 1990. Analysis of a disease transmission model in a population with varying size. J. Math. Biol., 28:257–270.
9. Busenberg, S., Cooke, K. L., and Thieme, H. R., 1991. Demographic change and persistence of HIV/AIDS in a heterogeneous population. SIAM J. Appl. Math., 51:1030–1052.
10. Clarke, C. W., 1976. Mathematical Bioeconomics:the Optimal Management of Renewable Resources, New York:Wiley.
11. Conrad, J. M., 2005. Open access and extinction of the passenger pigeon in North America. Nat. Res. Mod., 18:501–519.
12. Cushing, J. M., 1988. “ The Allee effect in age-structured population dynamics ”. In Mathematical Ecology, Edited by:Levin, S. A., and Hallam, T., 479–505. Teaneck, NJ:World Scientific Publishers.
13. Cushing, J. M., 1994. Oscillations in age-structured population models with an Allee effect. Oscillations in nonlinear systems:applications and numerical aspects. J. Comput. Appl. Math., 52:71–80.
14. de Castro, F., and Bolker, B., 2005. Mechanisms of disease-induced extinction, Ecol. Lett., 8:117–126.
15. Deredec, A., and Courchamp, F., 2006. Combined impacts of Allee effects and parasitism. Oikos, 112:667–679.
16. Drew, A., Allen, E. J., and Allen, L. J.S., 2006. Analysis of climate and geographic factors affecting the presence of chytridiomycosis in Australia. Dis. Aquat. Org., 68:245–250.
17. Emmert, K. E., and Allen, L. J.S., 2004. Population persistence and extinction in a discrete-time stage-structured epidemic model. J. Differ. Eqn Appl., 10:117–1199.
18. Emmert, K. E., and Allen, L. J.S., 2006. Population extinction in deterministic and stochastic discrete-time epidemic models with periodic coefficients with applications to amphibian populations. Nat. Res. Mod., 19:117–164.
19. Getz, W. M., and Pickering, J., 1983. Epidemic models:thresholds and population regulation. Amer. Nat., 121:892–898.
20. Greenhalgh, D., and Das, R., 1995. “ An SIRS epidemic model with a contact rate depending on population density ”. In Mathematical Population Dynamics:Analysis of Heterogeneity, Vol. One:Theory of Epidemics, Edited by:Arino, O., Axelrod, D., Kimmel, M., and Langlais, M., 79–101. Winnipeg:Wuerz.
21. Guckenheimer, J., and Holmes, P. J., 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, New York:Springer.
22. Hethcote, H. W., 2000. The mathematics of infectious diseases. SIAM Rev., 42:599–653.
23. Hilker, F. M., Langlais, M., and Malchow, H., to appear. The Allee effect and infectious diseases:extinction, multistability, and the (dis-)appearance of oscillations. Amer. Nat.
24. Hilker, F. M., Langlais, M., Petrovskii, S. V., and Malchow, H., 2007. A diffusive SI model with Allee effect and application to FIV. Math. Biosci., 206:61–80.
25. Hirsch, W. M., Hanisch, H., and Gabriel, J.-P., 1985. Differential equation models for some parasitic infections:methods for the study of asymptotic behavior. Comm. Pure Appl. Math., 38:733–753.
26. Jang, S. R.-J., 2006. Allee effects in a discrete-time host–parasitoid model. J. Differ. Eqn Appl., 12:165–181.
27. Jang, S. R.-J., 2007. Allee effects in a discrete-time host–parasitoid model with stage structure in the host. Discr. Cont. Dyn. Sys. Ser B, 12:145–159.
28. Jang, S. R.-J., and Diamond, S. L., 2007. A host–parasitoid interaction with Allee effects on the host. Comp. Math. Appl., 53:89–103.
29. Lafferty, K. D., and Gerber, L. R., 2002. Good medicine for conservation biology:the intersection of epidemiology and conservation theory. Conserv. Biol., 16:593–604.
30. Lloyd-Smith, J., Cross, P. C., Briggs, C. J., Daugherty, M., Getz, W. M., Latto, J., Sanchez, M. S., Smith, A. B., and Swei, A., 2005. Should we expect population thresholds for wildlife disease?. Trends Ecol. Evol., 20:511–519.
31. Malchow, H., Petroskii, S. V., and Venturino, E., 2008. Spatiotemporal Patterns in Ecology and Epidemiology:Theory, Models, and Simulation, Boca Raton:Chapman&Hall/CRC.
32. May, R. M., Anderson, R. M., and McLean, A. R., 1989. “ Demographic consequences of HIV/AIDS epidemics:II. Assuming HIV infection does not necessarily lead to AIDS ”. In Mathematical Approaches to Problems in Resource Management and Epidemiology, Edited by:Castillo-Chavez, C., Levin, S. A., and Shoemaker, C. A., 220–245. Berlin, Heidelberg:Springer. Lecture Notes in Biomathematics 81
33. McCallum, H., Barlow, N., and Hone, J., 2001. How should pathogen transmission be modelled?. Trends Ecol. Evol., 16:295–300.
34. Petrovskii, S. V., Morozov, A., and Li, B.-L., 2005. Regimes of biological invasions in a predator–prey system with the Allee effect. Bull. Math. Biol., 67:637–661.
35. Petrovskii, S. V., Morozov, A. Y., and Venturino, E., 2002. Allee effect makes possible patchy invasion in a predator–prey system. Ecol. Lett., 5:345–352.
36. Pounds, J. A., Bustamante, M. R., Coloma, L. A., Consuegra, J. A., Fogden, M. P.L., Foster, P. N., LaMarca, E., Masters, K. L., Merino-Viteri, A., Puschendorf, R., Ron, S. R., Sánchez-Azofeifa, G. A., Still, C. J., and Young, B. E., 2006. Widespread amphibian extinctions from epidemic disease driven by global warming. Nature, 439:161–167.
37. Rachowicz, L. J., Hero, J.-M., Alford, R. A., Taylor, J. W., Morgan, J. A.T., Vredenburg, V. T., Collins, J. P., and Briggs, C. J., 2005. The novel and endemic pathogen hypotheses:competing explanations for the origin of emerging infectious diseases of wildlife. Conserv. Biol., 19:1441–1448.
38. Rachowicz, L. J., Knapp, R. A., Morgan, J. A.T., Stice, M. J., Vredenburg, V. T., Parker, J. M., and Briggs, C. J., 2006. Emerging infectious disease as a proximate cause of amphibian mass mortality. Ecology, 87:1671–1683.
39. Salceanu, P. L., and Smith, H. L., to appear. Persistence in a discrete-time stage-structured epidemic model. J. Differ. Eqn Appl.
40. Skerrat, L. F., Berger, L., Speare, R., Cashins, S., McDonald, K. R., Phillott, A. D., Hines, H. B., and Kenyon, N., 2007. Spread of chytridiomycosis has caused the rapid global decline and extinction of frogs. EcoHealth, 4:125–134.
41. Stephens, P. A., Sutherland, W. J., and Freckleton, R. P., 1999. What is the Allee effect?. Oikos, 87:185–190.
42. Thieme, H. R., 1992. Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Math. Biosci., 111:99–130.
43. Thieme, H. R., 2003. Mathematics in Population Biology, Princeton:Princeton University Press.
44. van Voorn, G. A.K., Hemerik, L., Boer, M. P., and Kooi, B. W., 2007. Heteroclinic orbits indicate overexploitation in predator–prey systems with a strong Allee effect. Math. Biosci., 209:451–469.
45. Zhou, J., and Hethcote, H. W., 1994. Population size dependent incidence in models for diseases without immunity. J. Math. Biol., 32:809–834.