Annals of Applied Probability

The two-stage contact process

Stephen M. Krone

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We introduce a multitype interacting particle system, which is a natural generalization of the contact process. Here, individuals in the population have two life stages, young and adult. Only adults can give birth and each new offspring is young. Transition from young to adult occurs at constant rate, and individuals die at rates that depend on their life stage. Important to the analysis of this process is the construction of a multitype dual process.

Article information

Ann. Appl. Probab., Volume 9, Number 2 (1999), 331-351.

First available in Project Euclid: 21 August 2002

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Interacting particle system contact process multitype dual process survival


Krone, Stephen M. The two-stage contact process. Ann. Appl. Probab. 9 (1999), no. 2, 331--351. doi:10.1214/aoap/1029962745.

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  • DURRETT, R. 1988. Lecture Notes on Particle Sy stems and Percolation. Wadsworth, Belmont, CA.Z.
  • DURRETT, R. 1991. A new method for proving the existence of phase transitions. In Spatial Z. Stochastic Processes K. Alexander and J. Watkins, eds. 141 169. Birkhauser, Boston. ¨ Z.
  • DURRETT, R. and SCHONMANN, R. 1987. Stochastic growth models. In Percolation Theory and Z. Ergodic Theory of Infinite Particle Sy stems H. Kesten, ed. 85 119. Springer, New York. Z.
  • HANSKI, I. and ZHANG, D.-Y. 1993. Migration, metapopulation dy namics and fugitive coexistence. J. Theoret. Biol. 163 491 504.
  • HARRIS, T. 1972. Nearest neighbor Markov interaction processes on multidimensional lattices. Adv. Math. 9 66 89. Z.
  • HARRIS, T. 1974. Contact interactions on a lattice. Ann. Probab. 2 969 988. Z.
  • LIGGETT, T. 1985. Interacting Particle Sy stems. Springer, New York. Z.
  • NEUHAUSER, C. 1992. Ergodic theorems for the multity pe contact process. Probab. Theory Related Fields 91 467 506.