Persistence of host-parasite interactions in a disturbed environment

Journal of Theoretical Biology

Volumn 188, Issue 2, 1997, Pages 241-258

  Gubbins, Simon ^a   Gilligan, Christopher A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DISTURBANCE; HOST-PARASITE INTERACTION; PARASITE TRANSMISSION; SEASONAL DISTURBANCE;

ARTICLE; DISEASE TRANSMISSION; ENVIRONMENTAL FACTOR; HOST PARASITE INTERACTION; POPULATION DENSITY; POPULATION DYNAMICS; PRIORITY JOURNAL; SEASONAL VARIATION;

EID: 0031582767     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0466     Document Type: Article

References (52)

1. ANDERSON, R. M. & MAY, R. M. (1981). The population dynamics of microparasites and their invertebrate host. Phil. Trans. R. Soc. Lond. B291, 451-524.
2. ANDERSON, R. M. & MAY, R. M. (1986). The invasion, persistence and spread of infectious diseases within animal and plant communities. Phil. Trans. R. Soc. Lond. B314, 533-570.
3. ANDERSON, R. M. & MAY, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.
4. ANTONOVICS, J., IWASA, Y. & HASSELL, M. P. (1995). A generalized model of parasitoid, venereal and vector-based transmission processes. Amer. Nat. 145, 661-675.
5. BOLKER, B. & GRENFELL, B. T. (1995). Space, persistence and dynamics of measles epidemics. Phil. Trans. R. Soc. Lond. B348, 309-320.
6. BRIGGS, C. J. & GODFRAY, H. C. J. (1996). The dynamics of insect-pathogen interactions in seasonal environments. Theor. pop. Biol. 50, 149-177.
7. COOK, R. J. (1993). Making greater use of introduced micro-organisms for biological control of plant pathogens. Ann. Rev. Phytopath. 31, 53-80.
8. D'AMICO, V., ELKINTON, J. S., DWYER, G., BURAND, J. P. & BUONACCORSI, J. P. (1996). Virus transmission in gypsy moths is not a simple mass action process. Ecology 77, 201-206.
9. DEACON, J. W. (1988). Biocontrol of soil-borne pathogens with introduced inocula. Phil. Trans. R. Soc. Lond. B318, 249-264.
10. DIEKMANN, O. & KRETZSCHAMAR, M. (1991). Patterns in the effects of infectious diseases on population growth. J. math. Biol. 29, 539-570.
11. 0 in models for infectious diseases in heterogeneous populations. J. math Biol. 28, 365-382.
12. DIEKMANN, O., HEESTERBEEK, J. A. P. & METZ, J. A. J. (1995). The legacy of Kermack and McKendrick. In: Epidemic Models: Their Structure and Relation to Data (Mollison, D., ed.), pp. 95-115. Cambridge: Cambridge University Press.
13. DUSHOFF, J. (1996). Incorporating immunological ideas in epidemiological models. J. theor. Biol. 180, 181-187.
14. DWYER, G. & ELKINTON, J. S. (1993). Using simple models to predict virus epizootics in gypsy moth populations. J. anim. Ecol. 62, 1-11.
15. GLENDINNING, P. (1994). Stability, Instability and Chaos: an Introduction to the Theory of Nonlinear Differential Equations. Cambridge: Cambridge University Press.
16. GRENFELL, B. T., KLECZKOWSKI, A., ELLNER, S. P. & BOLKER, B. M. (1994). Measles as a case in non-linear forecasting and chaos. Phil. Trans. R. Soc. Lond. A348, 515-530.
17. GUBBINS, S. & GILLIGAN, C. A. (1996). Population dynamics of a parasite and hyperparasite in a closed system: model analysis and parameter estimation. Proc. R. Soc. Lond. B263, 1071-1078.
18. GUBBINS, S. & GILLIGAN, C. A. (1997). Biological control in a disturbed environment. Phil. Trans. R. Soc. Lond. B (in press).
19. GUCKENHEIMER, J. & HOLMES, P. (1983). Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Heidelberg: Springer-Verlag.
20. HANSKI, I., TURCHIN, P., KORPIMÄKI, E. & HENTTONEN, H. (1993). Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature, Lond. 364, 232-235.
21. HASSELL, M. P. (1981). Arthropod predator-prey systems. In: Theoretical Ecology (May, R. M., ed.) pp. 105-131. Oxford: Blackwell.
22. HASSELL, M. P., COMINS, H. N. & MAY, R. M. (1991). Spatial structure and chaos in insect population dynamics. Nature, Lond. 353, 255-258.
23. HASTINGS, A. & HIGGINS, K. (1994). Persistence of transients in spatially structured ecological models. Science 263, 1133-1136.
24. HEESTERBEEK, J. A. P. & ROBERTS, M. G. (1995a). Mathematical models for microparasites of wildlife. In: Ecology of Infectious Diseases in Natural Populations (Grenfell, B. T. & Dobson, A. P., eds), pp. 90-122. Cambridge: Cambridge University Press.
25. HEESTERBEEK, J. A. P. & ROBERTS, M. G. (1995b). Threshold quantities for helminth infections. J. math Biol. 33, 415-434.
26. HETHCOTE, H. W. & VAN DEN DRIESSCHE, P. (1991). Some epidemiological models with non-linear incidence. J. math Biol. 29, 271-287.
27. HOCHBERG, M. E. (1991). Non-linear transmission rates and the dynamics of infectious disease. J. theor. Biol. 153, 301-321.
28. HOCHBERG, M. E., HASSELL, M. P. & MAY, R. M. (1990). The dynamics of host-parasitoid-pathogen interactions. Amer. Nat. 135, 74-94.
29. HOLLING, C. S. (1959). The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Ent. 91, 293-320.
30. KENDALL, B. E., SCHAFFER, W. M. & TIDD, C. W. (1993). Transient periodicity in chaos. Phys. Lett. A177, 13-20.
31. KERMACK, W. O. & MCKENDRICK, A. G. (1927). Contributions to the mathematical theory of epidemics. Proc. R. Soc. Lond. A115, 700-721.
32. KLECZKOWSKI, A., BAILEY, D. J. & GILLIGAN, C. A. (1996). Dynamically generated variability in plant-pathogen systems with biological control. Proc. R. Soc. Lond. B263, 777-783.
33. LIU, W. M., HETHCOTE, H. W. & LEVIN, S. A. (1987). Dynamical behaviour of epidemiological models with non-linear incidence rates. J. math Biol. 25, 359-380.
34. LONDON, W. P. & YORKE, J. A. (1973). Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Am. J. Epidem. 98, 453-468.
35. MAY, R. M. (1977). Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature Lond. 269, 471-477.
36. MAY, R. M. (1981). Models for two interacting populations. In: Theoretical Ecology (May. R. M., ed.), pp. 78-104. Oxford: Blackwell.
37. MAY, R. M. & ANDERSON, R. M. (1979). Population biology of infectious diseases: Part II. Nature, Lond. 280, 455-461.
38. MOLLISON, D. (1986). Modelling biological invasions: chance, explanation and prediction. Phil. Trans. R. Soc. Lond. B314, 675-693.
39. MOLLISON, D. (1991). Dependence of epidemic and population velocities on basic parameters. Math. Biosci. 107, 255-287.
40. MOLLISON, D. & LEVIN, S. A. (1995). Spatial dynamics of parasitism. In: Ecology of Infectious Diseases in Natural Populations (Grenfell, B. T. & Dobson, A. P., eds), pp. 384-398. Cambridge: Cambridge University Press.
41. MURRAY, J. D. (1989). Mathematical Biology. Heidelberg: Springer-Verlag.
42. NASELL, I. (1995). The threshold concept in stochastic epidemic and endemic models. In: Epidemic Models: Their Structure and Relation to Data (Mollison, D., ed.), pp. 71-83. Cambridge: Cambridge University Press.
43. RAND, D. A. & WILSON, H. B. (1991). Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. Proc. R. Soc. Lond. B246, 179-184.
44. RENSHAW, E. (1991). Modelling Biological Populations in Space and Time. Cambridge: Cambridge University Press.
45. ROBERTS, M. G. & GRENFELL, B. T. (1991). The population dynamics of nematode infections of ruminants: periodic perturbations as a model for management. IMA J. Math. Appl. Med. Biol. 8, 83-93.
46. ROBERTS, M. G. & GRENFELL, B. T. (1992). The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living infective stages. IMA J. Math. Appl. Med. Biol. 9, 29-41.
47. RUXTON, G. D. & DOEBELI, M. (1996). Spatial self-organization and persistence of transients in a metapopulation model. Proc. R. Soc. Lond. B263, 1153-1158.
48. SCHAFFER, W. M., KENDALL, B. E. & TIDD, C. W. (1993). Transient periodicity and episodic predictability in biological dynamics. IMA J. Math. Appl. Med. Biol. 10, 227-247.
49. SCHWARTZ, I. B. (1985). Multiple recurrent outbreaks and predictability in seasonally forced non-linear epidemic models. J. math. Biol. 12, 347-361.
50. SHAW, M. W. (1994). Seasonally induced chaotic dynamics and their implications in models of plant disease. Plant Path. 43, 790-801.
51. SWINTON, J. & ANDERSON, R. M. (1995). Model frameworks for plant-pathogen interactions. In: Ecology of Infectious Diseases in Natural Populations (Grenfell, B. T. & Dobson, A. P., eds), pp. 280-294. Cambridge: Cambridge University Press.
52. WHITE, K. A. J., GRENFELL, B. T., HENDRY, R. J., LEJEUNE, O. & MURRAY, J. D. (1996). Effect of seasonal host reproduction on host-macroparasite dynamics. Math. Biosci. 137, 79-99.