A predator-prey model with disease in the prey

被引：422
作者：
Chattopadhyay, J
Arino, O
机构：
[1] Indian Stat Inst, Embryol Res Unit, Kolkata 700035, W Bengal, India
[2] Univ Pau, IPRA, UPRES A 5033, F-64000 Pau, France
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 1999年 / 36卷 / 06期
关键词：
sound prey; infected prey; predator; Hopf bifurcation; Poincare map;
D O I：
10.1016/S0362-546X(98)00126-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Three eco-epidemiological system species are considered: sound prey, infected prey, and predator. The system predator-prey model, where the prey is infected by a parasite, and the prey in turn infects the predator with that parasite, is described. The persistence and extinction conditions of the populations are derived and the conditions for which the system enters a Hopf-type bifurcation are determined. The bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a Holling-type II function.
引用
收藏
页码：747 / 766
页数：20
相关论文
共 21 条
  • [1] ANDERSON R M, 1991
  • [2] [Anonymous], 1980, LECT NOTES BIOMATHEM
  • [3] Bailey NT., 1975, MATH THEORY INFECT D
  • [4] De Jong M., 1994, Epidemic Models, their Structure and Relation to Data
  • [5] Diekmann O., 1994, Epidemic Models, their Structure and Relation to Data
  • [6] MATHEMATICAL-ANALYSIS OF SOME 3-SPECIES FOOD-CHAIN MODELS
    FREEDMAN, HI
    WALTMAN, P
    [J]. MATHEMATICAL BIOSCIENCES, 1977, 33 (3-4) : 257 - 276
  • [7] Greenhalgh D, 1995, Math. Popul. Dynam. Anal. Heterog., V1, P79
  • [8] PREDATOR-PREY POPULATIONS WITH PARASITIC INFECTION
    HADELER, KP
    FREEDMAN, HI
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1989, 27 (06) : 609 - 631
  • [9] HALE JK, 1982, METHODS BIFURCATION, V251
  • [10] HASSARD BD, 1981, LECT NOTES SERIES, V41
123