Persistence in a prey-predator system with disease in the prey

Journal of Biological Systems

Volumn 11, Issue 1, 2003, Pages 101-112

  Mukherjee, Debasis ^a  

^a VIVEKANANDA COLLEGE   (India)

Author keywords

Delay; Impermanence; Microparasite; Persistence; Prey predator; Switching

Indexed keywords

EID: 0142028741     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339003000634     Document Type: Article

References (19)

1. Anderson R. M. and May R. M., The invasion and spread of infectious diseases within animal and plant communities, Philos. Trans. R. Soc. Lond. B314 (1986) pp. 533-570.
2. Birkhoff G. and Rota G. C., Ordinary Differential Equations (Ginn, 1982).
3. Butler G. J., Freedman H. I. and Waltman P., Uniformly persistent systems, Proc. Am. Math. Soc. 96 (1986) pp. 425-430.
4. Dobson A. P., The population biology of parasite induced changes in host behavior, Q. Rev. Biol. 63 (1988) pp. 139-165.
5. Freedman H. I., A model of predator-prey dynamics as modified by the action of a parasite, Math. Biosci. 99 (1990) pp. 143-155.
6. Freedman H. I. and Waltman P., Persistence in models of three interacting predator-prey populations, Math. Biosci. 68 (1984) pp. 213-231.
7. Freedman H. I. and Waltman P., Persistence in a model of three competitive populations, Math. Biosci. 73 (1985) pp. 89-101.
8. Gard T. C., Persistence in food chains general interactions, Math. Biosci. 51 (1980) pp. 165-174.
9. Hadeler K. P. and Freedman H. I., Predator-prey populations with parasite infection, J. Math. Biol. 27 (1989) pp. 609-631.
10. Hale J. K. and Waltman P., Persistence in infinite dimensional systems, SIAM J. Math. Anal. 20 (1989) pp. 388-395.
11. Hofbauer J., General cooperation theorem for hypercycles, Monatsh. Math. 91 (1981) pp. 233-240.
12. Hofbauer J., Saturated equilibria, permanence and stability for ecological systems. In Mathematical Ecology, Proc. Trieste, ed. by Groos L., Hallam T. and Levin S. (World Scientific, Singapore, 1986).
13. Holmes J. C. and Bethel W. M., Modification of intermediate host behavior by parasite. In Behavioral Aspect of Parasite Transmission. Suppl. No. 1 to the Zool. J. Linnean Soc., ed. by Cunning E. V. and Wright C. A., 51 (1972) pp. 123-149.
14. Hutson V. and Law R., Permanent coexistence in general models of three interacting species, J. Math. Biol. 21 (1985) pp. 289-298.
15. Hutson V. and Vickers G. T., A criterion for permanent coexistence of species, with an application to a two prey one predator system, Math. Biosci. 63 (1983) pp. 253-269.
16. Kumar R. and Freedman H. I., A mathematical model of facultative mutualism with population interaction in a food chain, Math. Biosci. 97 (1989) pp. 235-261.
17. Mukherjee D., Uniform persistence in a generalized prey-predator system with parasitic infection, Biosystems 47 (1998) pp. 149-155.
18. Peterson R. O. and Page R. E., Wolf density as a predator of predation rate, Swedish Wildlife Research Suppl. 1 (1987) pp. 771-773.
19. Xiao Y. and Chen L., Modeling and analysis of a predator-prey model with disease in the prey, Math. Biosci. 171 (2001) pp. 59-82.