Analysis of a Three Species Eco-Epidemiological Model

Journal of Mathematical Analysis and Applications

Volumn 258, Issue 2, 2001, Pages 733-754

  Xiao, Yanni ^a   Chen, Lansun ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Global stability; Hopf bifurcation; Permanence; Predator prey model

Indexed keywords

EID: 0035877557     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2001.7514     Document Type: Article

References (17)

1. Hethcote H. W. A thousand and one epidemic models. Levin S. A. "Frontiers in Mathematical Biology". Lecture Notes in Biomathematics. 100:1994;504-515 Springer-Verlag, Berlin/Heidelberg, New York.
2. Anderso R. M., May R. M. Infectious Disease of Humans, Dynamics and Control. 1991;Oxford Univ. Press, London.
3. Bailey N. J. T. The Mathematical Theory of Infectious Disease and Its Applications. 1975;Griffin, London.
4. Diekmann O., Hecsterbeck J. A. P., Metz J. A. J. The legacy of Kermack and Mckendrick. Mollision D. Epidemic Models: Their Structure and Relation to Data. 1994;Cambridge Univ. Press, Cambridge.
5. Hadeler K. P., Freedman H. I. Predator-prey population with parasitic infection. J. Math. Biol. 27:1989;609-631.
6. Chattopadhyay J., Arino O. A predator-prey model with disease in the prey. Nonlinear Anal. 36:1999;749-766.
7. Venturino E. The influence of disease on Lotka-Volterra systems. Rockymount. J. Math. 24:1994;389-402.
8. J. C. Holmes and W. M. Bethel, Modification of intermediate host behavior by parasites, inBehavioural Aspects of Parasite Transmission (E. V. Canning and C. A. Wright, Eds.), Zool. f.Linnean Soc.51 Suppl. 1 1972, 123-149.
9. Peterson R. O., Page R. E. Wolf density as a predictor of predation rate. Swedish Wildlife Research Suppl. 1:1987;771-773.
10. Chen L. S., Chen J. Nonlinear Biological Dynamic Systems. 1993;Science Press, Beijing.
11. Anderson R. M., May R. M. The population dynamics of microparasites and their intervebrates hosts. Proc. Roy. Soc. Lond. B. 291:1981;451-463.
12. Nagumo N. Uber die Lage der Integralkurven gewonlicher Differantialgleichungen. Proc. Phys. Math. Soc. Japan. 24:1942;551-567.
13. Liu W. M. Criterion of Hopf bifurcation without using eigenvalues. J. Math. Anal. Appl. 182:1994;250-255.
14. Freedman H. I., Sree Hari Rao V. The trade-off between mutual interference and time lags in predator-prey-systems. Bull. Math. Biol. 45:1983;991-1003.
15. Hale J. K. Theory of Functional Differential Equations. 1977;Springer-Verlag, New York.
16. Kuang Y. Delay Differential Equations. 1993;Academic Press, San Diego.
17. Hale J. K., Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20:1989;388-396.