Journal of Mathematical Biology

, Volume 35, Issue 2, pp 129–157

The dynamics of infectious diseases in orchards with roguing and replanting as control strategy

  • Frank van den Bosch
  • André M. de Roos

DOI: 10.1007/s002850050047

Cite this article as:
van den Bosch, F. & de Roos, A. J Math Biol (1996) 35: 129. doi:10.1007/s002850050047


 Roguing and replanting is a widely adopted control strategy of infectious diseases in orchards. Little is known about the effect of this type of management on the dynamics of the infectious disease. In this paper we analyze a structured population model for the dynamics of an S-I-R type epidemic under roguing and replanting management. The model is structured with respect to the total number of infections and the number of post-infectious infections on a tree. Trees are assumed to be rogued, and replaced by uninfected trees, when the total number of infections on the tree reaches a threshold value. Stability analysis and numerical exploration of the model show that for specific parameter combinations the internal equilibrium can become unstable and large amplitude periodic fluctuations arise. Several hypothesis on the mechanism causing the destabilisation of the steady-state are considered. The mechanism leading to the large amplitude fluctuations is identified and biologically interpreted.

Key words: Structural population model Stability analysis Numerical solutions 

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Frank van den Bosch
    • 1
  • André M. de Roos
    • 2
  1. 1.Department of Mathematics, Agricultural University, Dreijenlaan 4, 6703 HA Wageningen, The NetherlandsNL
  2. 2.Department of Pure and Applied Ecology, University of Amsterdam, Kruislaan 320, 1098 SM Amsterdam, The NetherlandsNL