Multihost, multiparasite systems: An application of bifurcation theory

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 16, Issue 4, 1999, Pages 333-367

  Greenman, J V ^a   Hudson, P J ^a  

^a UNIVERSITY OF STIRLING   (United Kingdom)

Author keywords

Bifurcation; Coexistence; Epidemiology; Stability

Indexed keywords

ARTICLE; HOST; HOST PARASITE INTERACTION; MATHEMATICAL MODEL; PARASITOSIS; SUPERINFECTION; THEORY;

BIFURCATION; BIFURCATIONS THEORY; COEXISTENCE; EQUILIBRIUM STRUCTURES; LOCAL ANALYSIS; MODEL SIMPLIFICATION; NUMERICAL INVESTIGATIONS; PARAMETER SPACES; PARASITE-; QUALITATIVE PROPERTIES;

BIFURCATION (MATHEMATICS);

EID: 0033385389     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb16.4.333     Document Type: Article

References (26)

1. ANDERSON, R. M. & MAY, R. M. 1978 Regulation and stability of host-parasite population interactions: I regulatory processes. J. An. Ecol. 47, 219-247.
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. 314, 533-570.
3. BEGON, M. & BOWERS, R. G. 1992 Disease and community structure: The importance of host self-regulation in a host-parasite model. Am. Nat. 139, 1131-1150.
4. BEGUN, M. & BOWERS, R. G. 1995 Beyond host-parasite dynamics. In: Ecology of Infectious Diseases in Natural Populations (B. T. Grenfell & A. P. Dobson, eds.), pp. 478-509. Cambridge: Cambridge University Press.
5. BOWERS, R. G. & TURNER, J. 1997 Community structure and the interplay between interspecific infection and competition. J. Theor. Biol. 187, 95-109.
6. DOBSON, A. P. 1985 The population dynamics of competition between parasites. Parasitology 91, 317-347.
7. DOBSON, A. P. & HUDSON, P. J. 1992 Regulation and stability of a free-living host-parasite system: Trichostrongylus tenuis in red grouse. II. Population models. J. An. Ecol. 61, 487-498.
8. GANTMACHER, F. R. 1960 The Theory of Matrices, Vol. II. New York: Chelsea Publishing.
9. GREENMAN, J. V. & HUDSON, P. J. 1997 Infected coexistence instability with and without density-dependent regulation. J. Theor. Biol. 185, 345-356.
10. GREENMAN, J. V. & HUDSON, P. J. 1999 Host exclusion and coexistence in apparent and direct competition. Theor. Popul. Biol. 56, 48-64.
11. GREENMAN, J. V. & HUDSON, P. J. 2000 Parasite-mediated and direct competition in a two-host shared macroparasite system. Stirling Mathematical Ecology Group Working Paper. No. 15.
12. GRENFELL, B. T. & DOBSON, A. P. (eds.) 1995 Ecology of Infectious Diseases in Natural Populations. Cambridge: Cambridge University Press.
13. GUPTA, S., SWINTON, J. & ANDERSON, R. M. 1994 Theoretical studies of the effects of heterogeneity in the parasite population on the transmission dynamics of malaria. Proc. R. Soc. Lond. 256, 231-238
14. HOCHBERG, M. E. & HOLT, R. D. 1990 The coexistence of competing parasites. 1. The role of cross-species infection. Am. Nat. 136, 517-541
15. HOLT, R. D. & LAWTON, J. H. 1994 The ecological consequences of shared natural enemies. Ann. Rev. Ecol. Syst. 25, 495-520.
16. HOLT, R. D. & PICKERING, J. 1985 Infectious diseases and species coexistence: A model of Lotka-Volterra Form. Am Nat. 126, 196-211.
17. HUDSON, P. J. & GREENMAN. J. V. 1998 Competition mediated by parasites: Biological and theoretical progress. TREE 13, 387-390.
18. HUDSON, P. J. & GRENFELL, B. T. (eds.) 1999 The Ecology of Wildlife Diseases. Oxford: Oxford University Press. (In press.)
19. KUZNETSOV, Y. A. 1995 Elements of Applied Bifurcation Theory. New York: Springer.
20. MACDONALD, G. 1957 The Epidemiology and Control of Malaria London: Oxford University Press.
21. MAY, R. M. & ANDERSON, R. M. 1978 Regulation and stability of host-parasite population interactions: II destabilizing processes, J. An. Ecol. 47, 249-267.
22. MURRAY, J. D. 1993 Mathematical Biology. New York: Springer.
23. ROSS, R. 1916 An application of the theory of probabilities to the study of a priori pathometry. I. Proc. R. Soc. Lond. A92, 204-230.
24. WIGGINS, S. 1990 Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer.
25. WOLFRAM, S. 1988 Mathematica: A System for Doing Mathematics by Computer. Champaign, IL: Wolfram Research.
26. YAN, G. 1996 Parasite-mediated competition: A model of directly transmitted macroparasites. Am. Nat. 148, 1089-1112