Agriculture Reference
In-Depth Information
non-linear analysis of disease progress models allows additional parameters to be
estimated, like the maximum disease parameter
K
.
Usually, calendar time (days, weeks, etc.) is used as the independent variable
when fitting growth models to observed epidemic data. This is appropriate when the
research objective is not to compare epidemics between treatments. Otherwise, use
of time as an independent variable may result in incorrect conclusions if the host
growth patterns differ significantly between epidemics (treatments). For example,
suppose that all other data are the same except that the length of the host effective
growing season (i.e. period when host tissues are susceptible) at one site is 80% of
another site. It can be shown that the estimated apparent infection rate will be 25%
greater for the epidemic at the site with the shorter growing season than at the other
site. Although this analysis using time as an independent variable is technically
correct, careful interpretation is needed as the rate difference is not attributed to the
difference in disease development but rather to that in host growth pattern. We
might overcome this problem by expressing the time as a proportion of the growing
season and then using this 'biological time' as an independent variable when fitting
curves. This is particularly important when we are comparing different diseases
since the length of time for which host tissues are susceptible to infections may
differ significantly between pathogens. Lalancette and Hickey (1986) developed a
model that expressed the rate of disease change directly in terms of the change of
host size.
A potential limitation of using physical time as a measure of time is illustrated
by Lovell
et al.
(2004), who recommended instead the use of thermal time. Degree-
days have been used to model disease progress of
Verticillium
wilt in cotton
(Gutierrrez and DeVay, 1986), tomato powdery mildew (Correll
et al.
, 1988), wheat
take-all (Brasset and Gilligan, 1989; Colbach
et al.
, 1997; Schoeny and Lucas, 1999)
and potato early blight (Johnson and Teng, 1990). There are several implicit
assumptions associated with using degree-days. For example, it assumes that
temperature is the most important factor driving growth rates of host, pathogen and
disease and growth will stop if temperature is below the minimum or above the
maximum temperature threshold values. Use of degree-days is very common in
predicting spore maturity and subsequent discharge; for example, ascospores of
Venturia inaequalis
(cause of apple scab) (Gadoury
et al.
, 2004; see also Chapter
18) and apothecium production in
Sclerotinia sclerotiorum
(Sun and Yang, 2000).
8.3.2 Extensions to simple growth models
A growth model of two or three parameters often satisfactorily describes the
temporal disease dynamics. However, there are situations where such a simple
model may fail to capture the essential characteristics of the observed temporal
pattern. This is not surprising given the fact that the simple models ignore several
important factors that affect disease development, including host growth, fluctuating
environmental conditions (and their effect on the rate of disease increase) and the
length of latent and infectious periods. Significant advances have been made to
incorporate these factors into disease progress models.
