Effect of delay on a predator-prey model with parasitic infection

Nonlinear Dynamics

Volumn 63, Issue 3, 2011, Pages 311-321

  Yongzhen, Pei ^a   Shuping, Li ^a   Changguo, Li ^b  

^a TIANJIN POLYTECHNIC UNIVERSITY   (China)

^b Military Traffic Institute   (China)

Author keywords

Asymptotic stability; Bifurcation; Oscillations; Parasitic infection; Time delay

Indexed keywords

BIFURCATION; EPIDEMIC SYSTEM; NUMERICAL RESULTS; OSCILLATIONS; PARASITIC INFECTION; PARASITIC INFECTIONS; PERIODIC OSCILLATION; PREDATOR-PREY MODELS; PREY BIOMASS; SMALL AMPLITUDE; STEADY STATE;

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); ECOLOGY; POPULATION STATISTICS; TIME DELAY;

ASYMPTOTIC ANALYSIS;

EID: 79751534531     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9805-4     Document Type: Article

References (29)

1. P.J. Hudson A.P. Dobson K.D. Lafferty 2006 Is a healthy ecosystem one that is rich in parasites? Trends Ecol. Ev (Pubitemid 43947342)
2. Grenfell, B.T., Dobson, A.P.: Ecology of Infectious Diseases in Natural Populations. Cambridge University Press, Cambridge (1995)
3. Hudson, P.J., Rizzoli, A., Grenfell, B.T., Heesterbeek, H., Dobson, A.P.: The Ecology of Wildlife Diseases. Oxford University Press, Oxford (2001)
4. R.D. Holt A.P. Dobson M. Begon R.G. Bowers E.M. Schauber 2003 Parasite establishment in host communities Ecol. Lett. 6 837 842 10.1046/j.1461-0248. 2003.00501.x (Pubitemid 37105914)
5. S.M. Sait W.C. Liu D.J. Thompson H.C.J. Godfrey M. Begon 2000 Invasion sequence affects predator-prey dynamics in a multi-species interaction Nature 405 448 450 10.1038/35013045 (Pubitemid 30367419)
6. D. Mukherjee 2006 A delayed prey-predator system with parasitic infection Biosystems 85 158 164 10.1016/j.biosystems.2006.01.003 (Pubitemid 44016000)
7. M.H. Frank S. Kirsten 2008 Disease-induced stabilization of predator-prey oscillations J. Theor. Biol. 255 299 306 10.1016/j.jtbi.2008.07.038
8. M. Martcheva 2009 Evolutionary consequences of predation for pathogens in prey Bull. Math. Biol. 71 819 844 1163.92039 10.1007/s11538-008-9383-5 2505046
9. N. Xiao L. Chen 2001 Modelling and analysis of a predator-prey model with disease in the prey Math. Biosci. 171 59 82 0978.92031 10.1016/S0025-5564(01) 00049-9 1839209 (Pubitemid 32429043)
10. K.P. Hadeler H.I. Freedman 1989 Predator-prey populations with parasitic infection J. Math. Biol. 27 609 631 0716.92021 1024702
11. R.D. Holt M. Roy 2007 Predation can increase the prevalence of infectious disease Am. Nat. 169 690 699 10.1086/513188 (Pubitemid 46651172)
12. L. Han Z. Ma H.W. Hethcote 2001 Four predator prey models with infectious diseases Math. Comput. Model. 34 849 858 0999.92032 10.1016/S0895-7177(01) 00104-2 1858805 (Pubitemid 32930848)
13. S.A. Temple 1987 Do predators always capture substandard individuals disproportionately from prey populations? Ecology 68 669 674 10.2307/1938472
14. Holmes, J.C., Bethel, W.M.: Modification of intermediate host behavior by parasites. In: E.V. Canning, C.A. Wright (Eds.) Zool. J. Linn. Soc. 51(Suppl. I), 123-149 (1972)
15. P.J. Hudson A.P. Dobson D. Newborn 1992 Do parasites make prey more vulnerable to predation? Red grouse and parasites J. Anim. Ecol. 61 681 692 10.2307/5623 (Pubitemid 23397926)
16. 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. 6 797 802 10.1046/j.1461-0248.2003.00500.x (Pubitemid 37105907)
17. H.W. Hethcote W. Wang L. Han Z. Ma 2004 A predator-prey model with infected prey Theor. Popul. Biol. 66 259 268 10.1016/j.tpb.2004.06.010 (Pubitemid 39301179)
18. P. Driessche J. Watmough 2000 A simple SIS epidemic model with a backward bifurcation J. Math. Biol. 40 525 540 0961.92029 10.1007/s002850000032 1770939
19. Venturino, E.: Epidemics in predator-prey models: disease in the prey. In: Arino, O., Axelrod, D., Kimmel, M., Langlais, M. (Eds.) Mathematical Population Dynamics: Analysis of Heterogeneity. Theory of Epidemics, vol. 1, pp. 381-393. Wuerz Publishing, Winnipeg (1995)
20. X. Ji Y. Pei C. Li 2010 Two patterns of recruitment in an epidemic model with difference in immunity of individuals Nonlinear Anal., Real World Appl. 11 2078 2090 1197.34075 10.1016/j.nonrwa.2009.06.001 2646617
21. X. Li J. Wang M. Ghosh 2010 Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination Appl. Math. Model. 34 2 437 450 1185.34100 10.1016/j.apm.2009.06.002 2556194
22. Y. Li J. Cui 2009 The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage Commun. Nonlinear Sci. Numer. Simul. 14 2353 2365 10.1016/j.cnsns.2008.06.024 2474479
23. J. Chen X. Liu 2006 Stability of an seis epidemic model with constant recruitment and a varying total population size Appl. Math. J. Chin. Univ. Ser. B 21 1 1 8 1087.92052
24. C. Li Y. Pei Z. Liu 2010 A prey-predator system with parasitic infection and recovery J. Biomath. 25 1 1 5
25. M.J. Hatcher J.T.A. Dick A.M. Dunn 2006 How parasites affect interactions between competitors and predators Ecol. Lett. 9 1253 1271 10.1111/j.1461-0248. 2006.00964.x (Pubitemid 44571667)
26. F.D. Castro B.M. Bolker 2005 Parasite establishment and host extinction in model communities OIKOS 111 501 513 10.1111/j.1600-0706.2005.14101.x (Pubitemid 41802895)
27. R.O. Peterson R.E. Page 1987 Wolf density as a predictor of predation rate Swed. Wildlife Res. (Suppl.) 1 771 773
28. H.I. Freedman L.H. Erbe V.S.H. Rao 1986 Three species food chain model with mutual interference and time delays Math. Biosci. 80 57 80 0592.92024 10.1016/0025-5564(86)90067-2 849697
29. Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf-Bifurcation. Cambridge University Press, Cambridge (1981)