Journal of Mathematical Biology

, Volume 32, Issue 3, pp 251–268

Pathogen invasion and host extinction in lattice structured populations


  • Kazunori Satō
    • Department of Biology, Faculty of ScienceKyushu University
  • Hirotsugu Matsuda
    • Department of Biology, Faculty of ScienceKyushu University
  • Akira Sasaki
    • Department of Biology, Faculty of ScienceKyushu University

DOI: 10.1007/BF00163881

Cite this article as:
Satō, K., Matsuda, H. & Sasaki, A. J. Math. Biol. (1994) 32: 251. doi:10.1007/BF00163881


We examined the propagation of an infectious disease and the eventual extinction of the host population in a lattice-structured population. Both the host colonization and pathogen transmission processes are assumed to be restricted to act between the nearest neighbor sites. The model is analyzed by an improved version of pair approximation (IPA). Pair approximation is a technique to trace the dynamics of the number of nearest neighbor pairs having particular states, and IPA takes account of the clustering property of lattice models more precisely. The results are checked by computer simulations. The analysis shows: (i) in a one-dimensional lattice population, a pathogen cannot invade a host population no matter how large is the transmission rate; (ii) in a two-dimensional lattice population, pathogens will drive the host to extinction if the transmission rate is larger than a threshold. These results indicate that spatially structured population models may give qualitatively different results from conventional population models, such as Lotka-Volterra ones, without spatial structure.

Key words

Lattice modelHost extinctionPathogen invasionImproved pair approximation (IPA)Contact process

Copyright information

© Springer-Verlag 1994