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Pandemics of Focal Plant Disease: A Model


  • F. van den Bosch
  • J.A.J. Metz
  • J.C. Zadoks


An analytical model of a pandemic, initiated by a single focus and spreading over a continent, is developed, using foci as the smallest units of disease and fields as the smallest units of host. A few generalizing assumptions lead to a parameter sparse model which may answer general questions on pandemics in a qualitative manner. For pandemic spread of disease during one season a `within-season velocity of pandemic spread', C, is expressed in a set of integral equations. Reduction of inoculum during the off-season is expressed by a `survival ratio' of inoculum, epsilon. The effect of the off-season is a `push-back' of the pandemic front over a distance dh. It will be shown how dh is related to C and epsilon. The mean pandemic spread over successive years is calculated as the `polyetic velocity of pandemic spread', V, which depends on C and the push-back distance. The concept of `pandemic effectiveness' is parameterized. Relations between the two velocities of pandemic spread and several models are studied. Velocities of pandemic spread depend in a limited way on field density represented by the `cropping ratio' zeta. A general conclusion is that eradication and containment of a beginning pandemic becomes more difficult when the pandemic effectiveness of the disease is high, the tail of the spore dispersal probability distribution is long, the the sanitation during the off-season is poor, and the growing or epidemic season is long.

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  • F. van den Bosch & J.A.J. Metz & J.C. Zadoks, 1997. "Pandemics of Focal Plant Disease: A Model," Working Papers ir97083, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir97083

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    1. P. Muliere & P. Secchi, 1996. "Bayesian nonparametric predictive inference and bootstrap techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 663-673, December.
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