A predator-prey model with disease in the predator species only

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 4, 2010, Pages 2224-2236

  Haque, Mainul ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Eco epidemiological model; Infected predator; SIS epidemic model; Stability and bifurcation analysis

Indexed keywords

ABSOLUTE NUMBER; ALTERNATIVE SOURCE; ANALYTICAL RESULTS; BASIC REPRODUCTION NUMBER; BIOLOGICAL CONTROLS; EPIDEMIC MODELS; EPIDEMIOLOGICAL MODELS; EXPERIMENTAL DATA; INFECTED PREDATOR; LOGISTIC GROWTH; NUMERICAL SIMULATION; PARASITIC INFECTIONS; PREDATOR POPULATIONS; PREDATOR-PREY MODELS; STABILITY AND BIFURCATION ANALYSIS; THEORETICAL STUDY;

BIFURCATION (MATHEMATICS); DISEASE CONTROL;

MAMMALS;

EID: 77955631693     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.06.012     Document Type: Article

References (26)

1. M. Haque Ratio-dependent predator-prey models of interacting populations Bulletin of Mathematical Biology 71 2 2009 430 452
2. W. Kermack, and A. McKendrick A contribution to the mathematical theory of epidemics Proceedings of the Royal Society of London 115 1927 700 721
3. D. Minchella, and M. Scott Parasitism: A cryptic determinant of animal community structure Trends in Ecology & Evolution 6 8 1991 250 254
4. C. Gibson, and A. Watkinson The role of the hemiparasitic annual Rhinanthus minor in determining grassland community structure Oecologia 89 1 1992 62 68
5. A. Dobson, and M. Crawley Pathogens and the structure of plant communities Trends in Ecology & Evolution 9 10 1994 393 399
6. K. Hadeler, and H. Freedman Predator-prey populations with parasitic infection Journal of Mathematical Biology 27 6 1989 609 631
7. H. Freedman A model of predator-prey dynamics as modified by the action of a parasite Mathematical Biosciences 99 2 1990 143 155
8. E. Beltrami, and T. Carroll Modeling the role of viral disease in recurrent phytoplankton blooms Journal of Mathematical Biology 32 8 1994 857 863
9. E. Venturino The influence of diseases on LotkaVolterra systems Rocky Mountain Journal of Mathematics 24 1 1993 381 402
10. E. Venturino The effects of diseases on competing species Mathematical Biosciences 174 2 2001 111 131
11. E. Venturino Epidemics in predator-prey models: Disease in the predators Mathematical Medicine and Biology 19 3 2002 185 205
12. Y. Xiao, and L. Chen Modeling and analysis of a predator-prey model with disease in the prey Mathematical Biosciences 171 1 2001 59 82
13. H. Hethcote, W. Wang, L. Han, and Z. Ma A predator-prey model with infected prey Theoretical Population Biology 66 3 2004 259 268
14. M. Haque, and E. Venturino The role of transmissible diseases in the HollingTanner predator-prey model Theoretical Population Biology 70 3 2006 273 288
15. M. Haque, and E. Venturino An ecoepidemiological model with disease in predator: The ratio-dependent case Mathematical Methods in the Applied Sciences 30 14 2007
16. D. Greenhalgh, and M. Haque A predator-prey model with disease in the prey species only Mathematical Methods in the Applied Sciences 30 8 2007
17. M. Haque, J. Zhen, and E. Venturino An ecoepidemiological predator-prey model with standard disease incidence Mathematical Methods in the Applied Sciences 32 7 2009
18. M. van Baalen, V. Krivan, P. van Rijn, and M. Sabelis Alternative food, switching predators, and the persistence of predator-prey systems The American Naturalist 157 5 2001 512 524
19. F. Gulland The impact of infectious diseases on wild animal populations: A review Ecology of Infectious Diseases in Natural Populations 1 1995 20 51
20. R. Anderson, R. May, Population biology of infectious diseases, Report of the Dahlem workshop on population biology of infectious disease agents, 1982
21. H. Thieme Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations Mathematical Biosciences 111 1 1992 99 130
22. A. Bazykin, A. Khibnik, and B. Krauskopf Nonlinear Dynamics of Interacting Populations 1998 World Scientific
23. O. Diekmann, and J. Heesterbeek Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation 2000 Wiley
24. H. Hethcote The mathematics of infectious diseases SIAM Review 42 4 2000 599 653
25. F. Brauer, and C. Castillo-Chavez Mathematical Models in Population Biology and Epidemiology 2001 Springer
26. J. Ireland, R. Norman, and J. Greenman The effect of seasonal host birth rates on population dynamics: The importance of resonance Journal of Theoretical Biology 231 2 2004 229 238