On global and local critical points of extended contact process on homogeneous trees

Nobuaki Sugimine, Naoki Masuda, Norio Konno, Kazuyuki Aihara

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study spatial stochastic epidemic models called households models. The households models have more than two states at each vertex of a graph in contrast to the contact process. We show that, in the households models on trees, two thresholds of infection rates characterize epidemics. The global critical infection rate is defined by epidemic occurrence. However, some households may be eventually disease-free even for infection rates above the global critical infection rate, in as far as they are smaller than the local critical point. Whether the global one is smaller than the local one depends on the graph and the model. We show that, in the households models, the global one is smaller than the local one on homogeneous trees.

Original languageEnglish
Pages (from-to)13-17
Number of pages5
JournalMathematical Biosciences
Volume213
Issue number1
DOIs
Publication statusPublished - 2008 May
Externally publishedYes

Keywords

  • Global and local critical points
  • Households models

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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