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Asymptotic behaviour and threshold criteria in model plant disease epidemics
Author(s) -
JEGER M. J.
Publication year - 1986
Publication title -
plant pathology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.928
H-Index - 85
eISSN - 1365-3059
pISSN - 0032-0862
DOI - 10.1111/j.1365-3059.1986.tb02026.x
Subject(s) - confusion , differential equation , disease , biology , population , differential (mechanical device) , epidemic model , epidemiology , plant disease , epidemic disease , mathematics , statistics , mathematical analysis , pathology , medicine , environmental health , microbiology and biotechnology , physics , virology , psychoanalysis , thermodynamics , psychology
Two qualitative results concerning threshold criteria and asymptotic behaviour in plant disease epidemics are derived from Vanderplank's differential‐difference equation. Analysis shows the dependence of these results on initial disease and clarifies some confusion in the literature. Results from the deterministic theory of medical epidemics, based on linked differential equations describing the dynamics of different categories of diseased individuals, are compared with the results derived from the differential‐difference equation. Generally, the results correspond although the effects of initial disease need clarification. The need for a strict operational definition of the progeny‐parent ratio limits its present use in plant disease epidemiology. In particular the numerical value of the ratio is not a sufficient basis for distinguishing between endemic and epidemic disease. There is a need to link theory in plant disease epidemiology with similar theory in other areas of population biology. The use of linked differential equations, rather than the differential‐difference equation, provides a more flexible analytical tool.