An ecoepidemiological model with disease in predator: The ratio-dependent case

Mathematical Methods in the Applied Sciences

Volumn 30, Issue 14, 2007, Pages 1791-1809

  Haque, Mainul ^a   Venturino, Ezio ^b  

^a Krishnath College   (India)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Ecoepidemiology; Epidemic models; Global stability; Local stability; Persistence; Population models

Indexed keywords

BIOACTIVITY; GLOBAL OPTIMIZATION; NUMERICAL METHODS; POPULATION DYNAMICS;

ECOEPIDEMIOLOGY; LOCAL STABILITY;

DISEASE CONTROL;

EID: 34548403752     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.869     Document Type: Conference Paper

References (34)

1. Venturino E. Epidemics in predator-prey models: disease in the prey. In Mathematical Population Dynamics, Analysis of Heterogeneity, Arino O, Axelrod D, Kimmel M, Langlais M (eds), vol 1, Theory of Epidemics. Wuertz Publishing Ltd.: Winnipeg, Canada, 1995; 381-393.
2. Venturino E. The effects of diseases on competing species. Mathematical Biosciences 2001; 174:111-131.
3. Venturino E. Epidemics in predator-prey model: disease in the predators. IMA Journal of Mathematics Applied in Medicine and Biology 2002; 19:185-205.
4. Venturino E. How diseases affect symbiotic communities. Mathematical Biosciences 2007; 206(1): 11-30.
5. Haque M, Venturino E. Increase of the prey may decrease the healthy predator population in presence of a disease in the predator. Hermis 2006; 7:38-59.
6. Haque M, Venturino E. The role of transmissible diseases in Holling-Tanner predator-prey model. Journal of Theoretical Population Biology 2006; 70(3):273-288.
7. Abrams PA. The fallacies of ratio-dependent predation. Ecology 1994; 75(6): 1842-1850.
8. Abrams PA, Ginzburg LR. The nature of predation: prey dependent, ratio dependent or neither? Trends in Ecology and Evolution 2000; 15:337-341.
9. Akcakaya HR. Population cycles of mammals: evidence for ratio-dependent predator-prey hypothesis. Ecological Monographs 1992; 62:119-142.
10. Hsu SB, Hwang TW, Kuang Y. Rich dynamics of ratio-dependent one prey two predators model. Journal of Mathematical Biology 2001; 43:377-396.
11. Hsu SB, Hwang TW, Kuang Y. Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system. Journal of Mathematical Biology 2001; 42:490-506.
12. Hsu SB, Hwang TW, Kuang Y. A ratio-dependent food chain model and its application to biological control. Mathematical Biosciences 2003; 181:55-83.
13. Hairston NG, Smith FE, Slobodkin LB. Community structure, population control and competition. American Naturalist 1960; 94:421-425.
14. Rosenzweig ML. Paradox of enrichment: destabilization of exploitation systems in ecological times. Science 1971; 171:385-387.
15. Abrams PA, Walter CJ. Invulnerable prey and the paradox of enrichment. Ecology 1996; 77:1125-1133.
16. Luck RF. Evaluation of natural enemies for biological control: a behavior approach. Trends in Ecology and Evolution 1990; 5:196-199.
17. Arditi R, Berryman AA. The biological control paradox. Trends in Ecology and Evolution 1991; 6:32.
18. May RM. Theoretical Ecology (2nd edn). Blackwell: Oxford, U.K., 1981.
19. Oksanen T, Power ME, Oksanen L. Habitat selection and consumer resources. American Naturalist 1995; 146:565-583.
20. Oksanen T, Oksanen L, Jedrzejewski W, Jedrzejewska B, Korpimáki E, Norrdahl K. Predation and the dynamics of the bank vole Clethrionomys glareolus. In Bank Vole Biology; Recent Advances in the Population Biology of a Model Species, Hansson L, Bujalska G (eds). Poland Journal of Ecology 2000; 48(suppl): 197-217.
21. Oksanen T, Schneider M, Rammul Ü, Hambäck PA, Aunapuu M. Population fluctuations of voles in NortFennoscandian tundra: contrasting dynamics in adjacent areas with different habitat composition. Oikos 1999; 86:463-478.
22. Oksanen T, Oksanen L, Schneider M, Aunapuu M. Regulation cycles and stability in Northern carnivore-herbivore systems: back to first principles. Oikos 2001; 94:101-117.
23. Turchin P, Oksanen L, Ekerholm P, Oksanen T, Henttonen H. Are lemmings prey or predator? Nature 2000; 405:562-564.
24. Oksanen L, Oksanen T. The logic and realism of the hypothesis of exploitation ecosystems. American Naturalist 2000; 155:703-723.
25. Arditi R, Ginzburg LR, Akcakaya HR. Variation in plankton densities among lakes: a case fraction dependent models. American Naturalist 1991; 138:1287-1296.
26. Gutierrez AP. The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson's blowflies as an example. Ecology 1992; 73:1552-1563.
27. Xiao D, Ruan S. Global dynamics of ratio-dependent predator-prey system. Journal of Mathematical Biology 2001; 43:268-290.
28. Arino O, El Abdllaoui A, Mikram J, Chattopadhyay J. Infection on prey population may act as a biological control in ratio-dependent predator-prey model. Nonlinearity 2004; 17:1101-1116.
29. Hale J, Koçaz H. Dynamics and Bifurcations. Springer: Berlin, 1991.
30. Jost C, Arditi R. Identifying predator-prey process from time series. Theoretical Population Biology 2000; 57: 325-337.
31. Kuang Y, Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. Journal of Mathematical Biology 1998; 35:389-406.
32. Follmann EH, Ritter DG, Hartbauer DW. Gral vaccination of captive artic foxes with lyophilized SAG2 rabies vaccine. Journal of Wildlife Diseases 2004; 40:328-334.
33. Ishikawa H, Ohga Y, Doi R. A model for the transmission of Echinococcus multilocularis in Hokkaido, Japan. Parasitology Research 2003; 91:444-451.
34. Mebatsion T. Extensive attenuation of rabies virus by simultaneously modifying the Dynein light chain binding site in the P protein and replacing Arg333 in the G protein. Journal of Virology 2001; 75:11496-11502.