A model of predator-prey dynamics as modified by the action of a parasite.

A predator-prey population is described in which the prey population may be either a secondary host or a primary host to a parasite, but the predator is always a primary host. Those prey that have been invaded by the parasite have their behavior modified so as to make them more susceptible to predation. The model is described by a system of three autonomous ordinary differential equations. Conditions for persistence of all populations are given in the case that both populations are primary hosts. A brief discussion of the stability of the interior equilibrium is given.

[1]  H. I. Freedman.  Deterministic mathematical models in population ecology , 1982 .

[2]  R. May,et al.  Regulation and Stability of Host-Parasite Population Interactions: I. Regulatory Processes , 1978 .

[3]  M. Rau,et al.  Parasite-induced susceptibility of moose to hunting , 1979 .

[4]  H. I. Freedman,et al.  Obligate mutualism with a predator: Stability and persistence of three-species models☆☆☆★ , 1987 .

[5]  J. Tiner.  The migration, distribution in the brain, and growth of ascarid larvae in rodents. , 1953, The Journal of infectious diseases.

[6]  C. Arme,et al.  Infections of the three-spined stickleback, Gasterosteus aculeatus L., with the plerocercoid larvae of Schistocephalus solidus (Müller, 1776), with special reference to pathological effects , 1967, Parasitology.

[7]  Paul Waltman,et al.  Uniformly persistent systems , 1986 .

[8]  H. I. Freedman,et al.  Predator influence on the growth of a population with three genotypes , 1978 .

[9]  P. Waltman.  Deterministic Threshold Models in the Theory of Epidemics , 1974, Lecture Notes in Biomathematics.

[10]  H. I. Freedman,et al.  Predator-prey populations with parasitic infection , 1989, Journal of mathematical biology.

[11]  A. Dobson,et al.  The Population Biology of Parasite-Induced Changes in Host Behavior , 1988, The Quarterly Review of Biology.

[12]  H. I. Freedman,et al.  Persistence in models of three interacting predator-prey populations , 1984 .

[13]  Roy M. Anderson,et al.  REGULATION AND STABILITY OF HOST-PARASITE POPULATION INTERACTIONS , 1978 .

[14]  J. Tiner.  The Fraction of Peromyscus leucopus Fatalities Caused by Raccoon Ascarid Larvae , 1954 .

[15]  Joseph W.-H. So,et al.  Global stability and persistence of simple food chains , 1985 .

[16]  R M May,et al.  The invasion, persistence and spread of infectious diseases within animal and plant communities. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.