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Zbl 0865.92017
van den Bosch, Frank; de Roos, André M.
(van den Bosch, Frank; de Roos, André M.)
The dynamics of infectious diseases in orchards with roguing and replanting as control strategy. (English)
[J] J. Math. Biol. 35, No.2, 129-157 (1996). ISSN 0303-6812; ISSN 1432-1416/e

Summary: 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. 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 postinfectious 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 hypotheses 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.

MSC 2000:: *92D30 Epidemiology

Keywords: structural population model; stability analysis; numerical solutions; S-I-R type epidemic

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Zentralblatt MATH Berlin [Germany]