Agriculture Reference
In-Depth Information
The explicit relationship of
R
with
r
for an entire epidemic in terms of
y
0
,
i
,
p
and
t
was discovered by Jeger (1984).
R
is an important parameter in determining when an
epidemic can occur: in particular
iR
> 1 is necessary for an epidemic to occur (Jeger,
1986).
Another flexible and biologically intuitive approach to incorporate disease
components is the use of linked differential equations. Often this approach may
suffer from the difficulty in obtaining an analytical solution and hence numerical
integration may be necessary. However, steady-state analysis of these equations may
generate important results, for example, on criteria for persistence and invasion.
Fitting a set of linked differential equations to a set of observed data is not a trivial
matter though significant progress has been made in this area. For example, three
linked differential equations can be used to describe the dynamics of disease
components (latent -
y
l
, infectious -
y
i
, removed -
y
r
):
⎧
dy
l
dt
(
)
−
=
bHy
i
1
−
y
i
−
y
r
−
y
l
gy
l
⎪
⎪
(8.8)
dy
i
dt
⎨
=
gy
l
−
hy
i
⎪
⎪
dy
r
dt
=
hy
i
⎩
where
b
,
g
and
h
are the infection, latent and infectious rate, respectively. This
approach is very flexible, for example, it may allow rate parameters (
b
,
g
,
h
etc.) to
be of any form of functions of other variables. As discussed before, host growth can
also be included. Using this approach, Jeger (1982, 1984, 1986) successfully
established the criteria for the establishment and subsequent spread of an epidemic,
and the relationships among various components of the disease. This approach has
been widely used in theoretical modelling of disease development for both soil- and
air-borne pathogens, and virus diseases (Chan and Jeger, 1994; Gilligan
et al.
, 1997;
Jeger
et al.
, 1998; Jeger, 2000; Madden
et al.
, 2000; Paulitz, 2000; Gilligan, 2002;
Bailey and Gilligan, 2004; Bailey
et al.
, 2004; Jeger
et al.
, 2004a). A forecasting
system for apple powdery mildew has been developed on the basis of this approach
(Xu, 1999a).
8.3.3 Area under the disease progress curve (AUDPC)
AUDPC is the amount of disease integrated between two times of interest and is
calculated without regard to curve shape (Shaner and Finney, 1977). This approach
of summarising disease progress data into one value is appropriate when damages to
host are proportional to the total amount and duration of the disease. However, if
crop loss is related to a particular phase of the epidemic, for instance, during the
blossom period, then AUDPC summarised over the period other than just over the
particular period may lead to misleading conclusions. AUDPC can be a very useful
alternative to fitting growth models, particularly if observed disease progress
patterns cannot be fitted into simple growth models. Such situations can arise
