Models developed in continuous-time have been used to study the epidemiology and
population dynamics of plant hosts, usually in cultivated systems. Here discrete-time
SIR–type models are developed which contain parameters representing characteristics of
an uncultivated, biennial host plant – systemic, castrating pathogen system. This thesis
presents 4 epidemiological model forms representing a generic SIR model, a constant
pathogen-induced mortality model, a variable pathogen-induced mortality model, and a
model which has an additional phase representing a seedbank. Using a range of
parameter values it is possible to produce simulation outcomes with population crashes,
cycles and steady-state populations. For each of the models a pathogen epidemic
criterion is derived as is a term describing population steady-state values. For the
pathogen-induced mortality models, the invasion criteria include a pathogenicity term
indicating that the pathogen in part regulates the host population dynamics.
The biennial host plant Tragopogon pratensis has been recorded in the Park Grass
Experiment and has been described as an outbreak species regulated by the autoecious,
demicyclic rust fungus, Puccinia hysterium (Silvertown et al., 2006). The rust is shown
to castrate the host plant by reducing the numbers of seed set and the viability of seeds
produced by infected individuals. Further characteristics of this host – pathogen system
are identified by using the developed models. This is justified as the recurrencerelationships
derived from the models fit the observed data, and that the accuracy of the
fit is increased with larger values of pathogen-induced mortality. These models produce
simulation outcomes that are similar to the host population dynamics. The models also
show that the system is governed by density-dependent factors.