Impacts of incubation delay on the dynamics of an eco-epidemiological system - A theoretical study

Bulletin of Mathematical Biology

Volumn 70, Issue 7, 2008, Pages 2017-2038

  Bairagi, N ^a   Sarkar, R R ^b   Chattopadhyay, J ^c  

^a JADAVPUR UNIVERSITY   (India)

^b CENTRE FOR CELLULAR AND MOLECULAR BIOLOGY   (India)

^c INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Delay; Holling type II; Hopf bifurcation; Infected population; Linear mass action; Local stability; Predator; Susceptible population

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMPUTER SIMULATION; DISEASE TRANSMISSION; ECOSYSTEM; HOST PARASITE INTERACTION; PARASITOLOGY; PARASITOSIS; POPULATION DENSITY; POPULATION DYNAMICS; PREDATION;

ALGORITHMS; ANIMALS; BASIC REPRODUCTION NUMBER; COMPUTER SIMULATION; ECOSYSTEM; HOST-PARASITE INTERACTIONS; MODELS, BIOLOGICAL; PARASITIC DISEASES; POPULATION DENSITY; POPULATION DYNAMICS; PREDATORY BEHAVIOR;

EID: 52549118659     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9337-y     Document Type: Article

References (45)

1. V.D. Adams D.L. De Angelis R.A. Goldstein 1980 Stability analysis of the time delay in a host parasitoid model J. Theor. Biol. 83 43 62
2. Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans-Dynamics and Control. Oxford University Press, London.
3. Arriola, L., Hyman, J., 2005. Lecture Notes, Forward and Adjoint Sensitivity Analysis: with Applications in Dynamical Systems, Linear Algebra and Optimization. Mathematical and Theoretical Biology Institute.
4. J. Chattopadhyay O. Arino 1999 A predator-prey model with disease in the prey Nonlinear Anal. 36 747 766
5. J. Chattopadhyay N. Bairagi 2001 Pelicans at risk in Salton Sea-an eco-epidemiological study Ecol. Model. 136 103 112
6. J.P. Cohn 2000 Saving the Salton Sea Bioscience 50 4 295 301
7. + T-cells Math. Biosci. 165 27 39
8. R.V. Culshaw S. Ruan G. Webb 2003 A mathematical model of cell to cell spread of HIV-1 that includes a time delay J. Math. Biol. 46 425 444
9. Curio, E., 1988. Behavior and parasitism. In: Mehlhorn, H. (Ed.), Parasitology in Focus. Springer, New York.
10. Dieudonne', J., 1960. Foundations of Modern Analysis. Academic, New York.
11. A.P. Dobson P.J. Hudson 1992 Regulation and stability of a free-leaving host-parasite system, Trichostrongylus tenuis in red grouse. II. Population models J. Anim. Ecol 61 487 500
12. G. Dwyer J. Dushoff S.H. Yee 2004 Generalist predators, specialist pathogens and insect outbreaks Nature 43 341 345
13. A. Fenton S.A. Rands 2006 The impact of parasite manipulation and predator foraging behavior on predator-prey communities Ecology 87 11 2832 2841
14. H.I. Freedman V.S.H. Rao 1983 The trade-off between mutual interference and time-lags in predator-prey systems Bull. Math. Biol. 45 991
15. H.I. Freedman J.F. Addicot B. Rai 1987 Obligate mutualism with a predator: stability and persistence of three species models Theor. Popul. Biol. 32 157 175
16. W.J. Freeland 1983 Parasites and coexistence of animal host species Am. Nat. 121 223 236
17. M. Friend 2002 Avian disease in the Salton Sea Hydrobiologia 473 293 806
18. M.R. Gonzalez C.M. Hart J.R. Verfaillie S.H. Hurlbert 1998 Salinity and fish effects on Salton Sea microecosystems: water chemistry and nutrient cycling Hydrobiologia 381 105 128
19. Gopalsamy, K., 1992. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht.
20. K.P. Hadeler H.I. Freedman 1989 Predator-prey population with parasite infection J. Math. Biol. 27 609 631
21. Hassard, B.D., Kazarinoff, N.D., Wan, Y.H., 1981. Theory and Application of Hopf Bifurcation. Cambridge University Press, Cambridge.
22. Hethcote, H.W., Levin, S.A., 1989. Periodicity in epidemiological models. In: Gross, L., Levin, S.A. (Eds.), Applied Mathematical Ecology, pp. 193-211. Springer, New York.
23. Holling, C.S., 1965. The functional response... population regulation. Memories of the entomological society of Canada, 45, pp. 1-60.
24. Holmes, J.C., Bethel, W.M., 1972. Modification of intermediate host behavior by parasites. In: Canning, E.V., Wright, C.A. (Eds.), Behavioral Aspects of Parasite Transmission. Suppl. I to Zool. f. Linnean Soc., vol. 51, pp. 123-149.
25. Horvitz, S., 1999, http://www.sci.sdsu.edu/salton/ Salton%20Sea%20Description.html.
26. P.J. Hudson A.P. Dobson D. Newborn 1992 Do parasites make pray vulnerable to predation? Red grouse and parasites J. Anim. Ecol. 61 681 692
27. P.J. Hudson D. Newborn A.P. Dobson 1992 Regulation and stability of a free-leaving host-parasite system, Trichostrongylus tenuis in red grouse. I. Monitoring and parasite reduction experiment J. Anim. Ecol. 61 477 486
28. P.J. Hudson A.P. Dobson D. Newborn 1998 Prevention of population cycles by parasite removal Science 282 2256 2258
29. A.R. Ives D.L. Murray 1997 Can sublethal parasitism destabilize predator-prey population dynamics? a model of snowshoe hares predators, and parasites J. Anim. Ecol. 66 265 278
30. J.R. Jehl 1996 Mass mortality events of eared grebes in North America Am. J. Field Ornithol. 67 3 471 476
31. J. Kaiser 1999 Salton Sea: Battle over a dying sea Science 284 5411 28 30
32. Kuang, Y., 1993. Delay Differential Equations with Applications in Population Dynamics. Academic, New York.
33. K.D. Lafferty 1992 Foraging on prey that are modified by parasites Am. Nat. 140 854 867
34. K.D. Lafferty A.K. Morris 1996 Altered behaviour of parasitized killifish increases susceptibility to predation by bird final hosts Ecology 77 1390 1397
35. MacDonald, M., 1978. Time Delays in Biological Models. Springer, Heidelberg.
36. MacDonald, M., 1989. Biological Delay Systems: Linear Stability Theory. Cambridge University Press, Cambridge.
37. H. McCallum D. Harvell A. Dobson 2003 Rates of spread of marine pathogen Ecol. Lett. 6 1062 1067
38. H.I. McCallum 2004 Does terrestrial epidemiology apply to marine systems? Trends Ecol. Evol. 19 11 585 591
39. D. Minchella M.E. Scott 1991 Parasitism: A cryptic determinant of animal community structure Trends Ecol. Evol. 6 250 254
40. Moore, J., 2002. Parasites and the Behaviour of Animals. Oxford University Press, Oxford.
41. C. Packer R.D. Holt P.J. Hudson K.D. Lafferty A.P. Dobson 2003 Keeping the herds healthy and alert: implications of predator control for infectious disease Ecol. Lett. 6 792 802
42. Slack, G., 1997. Salton Sea Sickness. Pacific Discovery, Winter.
43. Tompkins, D.N., et al., 2002. Parasites and host population dynamics. In: Hudson, P.J., Rizzoli, A., Grenfell, B.T., Heesterbeek, H., Dobson, A.P. (Eds.), The Ecology of Wildlife Disease, pp. 45-62. Oxford University Press, Oxford
44. F. Thomas F. Cezilly T.D. Meeus A. Crivelli F. Renaud 1997 Parasitism and ecology of wetlands: a review Estuaries 20 3 646 654
45. E. Venturino 2002 Epidemics in predator-prey models: disease in the predators IMA J. Math. Appl. Med. Biol. 19 185 205