Epidemics of Plant Diseases: Mathematical Analysis and by J. Kranz (auth.), Professor Dr. Jürgen Kranz (eds.)

By J. Kranz (auth.), Professor Dr. Jürgen Kranz (eds.)

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3 I m 'Y2(1-YI) --g t2-tl YI(1-Y2) (21) Another concept which is offered by VAN DER PLANK (1960, 1963), is the basic infection rate, which is no longer based on the proportion Yt of diseased susceptible host tissue alone, but on that proportion of y which has passed the latent period and thus has become infectious and dy/ dt = RYt-p(l - Yt) (22) R = lIYo(t2 - t l ) (in 111 - Y2 - In 111 - YI) (23) The Role and Scope of Mathematical Analysis and Modeling in Epidemiology 31 where R = basic infection rate, Yo = initial disease, Yt = disease at time t, and = proportion of disease that has passed the latent period p.

Ecology of plant pathogens in soil. VII. Mathematical models and inoculum density. Phytopathology 57, 662--666 (1967). BALD,]. : Measurement of host reactions to soil-borne inoculum. In: Root diseases and soilborne pathogens. (ed. A. TOUSSOUN, R. E. 37-41. Berkeley, Los Angeles, London: Univ. of California Press 1970. : Beitrage zur Epidemiologie von Cercospora beticola Sacco an Zuckerriiben. D. Thesis Univ. Bonn (1971).

Growth functions from which models for transformation of disease progress curves can be derived, by the way, apparently have a wide scope, as shown by ANALYTIS (1973, Tables 2 and 3). for more details on growth functions see JOWETT et al. 3 Populations Changing in Time Time aspects so far have met the greatest interest in epidemiology, as reflected by the published evidence. This mostly refers to the progress of disease, either within a pathogens generation (cycle) or as polycyclic diseases within a vegetation period, year, or any other time unit.

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