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February 1997 Predator-prey and host-parasite spatial stochastic models
Rinaldo B. Schinazi
Ann. Appl. Probab. 7(1): 1-9 (February 1997). DOI: 10.1214/aoap/1034625250


We consider two interacting particle systems on $\mathbf{Z}^d$ to model predator-prey and host-parasite interactions. In both models we have two types of $\mathbf{Z}^d$ particles (1 and 2) and each site in can be in one of four states: empty, occupied by a type 1 particle, occupied by a type 2 particle or occupied by two particles (one of each type). Each type gives birth to particles of the same type on nearest neighbor sites. The interaction between the two types of particles occurs only when a site is occupied by one particle of each type. For both models we show that coexistence and noncoexistence are possible in any dimension.


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Rinaldo B. Schinazi. "Predator-prey and host-parasite spatial stochastic models." Ann. Appl. Probab. 7 (1) 1 - 9, February 1997.


Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0880.60099
MathSciNet: MR1428747
Digital Object Identifier: 10.1214/aoap/1034625250

Primary: 60K35

Keywords: host-parasite , interacting particle systems , Predator-prey

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 1 • February 1997
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