Understanding chicken walks on n × n grid

Hamiltonian paths, discrete dynamics, and rectifiable paths

Arni S R Rao, Fiona Tomley, Damer Blake

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Understanding animal movements and modeling the routes they travel can be essential in studies of pathogen transmission dynamics. Pathogen biology is also of crucial importance, defining the manner in which infectious agents are transmitted. In this article, we investigate animal movement with relevance to pathogen transmission by physical rather than airborne contact, using the domestic chicken and its protozoan parasite Eimeria as an example. We have obtained a configuration for the maximum possible distance that a chicken can walk through straight and nonoverlapping paths (defined in this paper) on square grid graphs. We have obtained preliminary results for such walks which can be practically adopted and tested as a foundation to improve understanding of nonairborne pathogen transmission. Linking individual nonoverlapping walks within a grid-delineated area can be used to support modeling of the frequently repetitive, overlapping walks characteristic of the domestic chicken, providing a framework to model fecal deposition and subsequent parasite dissemination by fecal/host contact. We also pose an open problem on multiple walks on finite grid graphs. These results grew from biological insights and have potential applications.

Original languageEnglish (US)
Pages (from-to)3346-3358
Number of pages13
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number15
DOIs
StatePublished - Oct 1 2015

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Hamiltonians
Discrete Dynamics
Hamiltonian path
Pathogens
Walk
Grid
Path
Grid Graph
Animals
Contact
Finite Graph
Modeling
Straight
Linking
Biology
Overlapping
Open Problems
Configuration
Parasites

Keywords

  • Eimeria
  • NP-complete
  • longest paths
  • maximum walks
  • spread of bird diseases

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Understanding chicken walks on n × n grid : Hamiltonian paths, discrete dynamics, and rectifiable paths. / Rao, Arni S R; Tomley, Fiona; Blake, Damer.

In: Mathematical Methods in the Applied Sciences, Vol. 38, No. 15, 01.10.2015, p. 3346-3358.

Research output: Contribution to journalArticle

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