Mathematical modelling of induced resistance to plant disease : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany campus, New Zealand
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Date
2014
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Massey University
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Abstract
The underlying theory of induced resistance (IR) is concerned with the situation
when there is an increase in plant resistance to herbivore or pathogen attack that
results from a plant's response triggered by an agent such as elicitors (also known
as \plant activators"). This mechanism has been well studied in plant pathology
literature. In this thesis, a mathematical model of induced resistance mechanism
using elicitors is proposed and analysed. An adaptation of traditional Susceptible-
Infected-Removed (SIR) model, this proposed model is characterised by three main
compartments, namely: susceptible, resistant and diseased. Under appropriate environmental
conditions, susceptible plants (S) may become diseased (D) when it is
exposed to a compatible pathogen or able to resist the infection (R) via basal host
defence mechanisms. The application of an elicitor enables the signal activation of
plant defence genes to enhance the basal defence responses and thereby a ecting the
relative proportion of plants in each of the S, R and D compartments. In literature,
induced resistance is described as a transient response and this scenario is modelled
using reversible processes to describe the temporal evolution of the compartments.
The terms in the equations introduce parameters which are determined by tting
the model to matching experimental data sets using MATLAB \fminsearch". This
then gives the model's outcome to predict the relative proportion of plants in each
compartment and quantitatively estimates the elicitor e ectiveness. Extensions of
the model are developed, which includes some factors that a ect the performance of
IR such as elicitor concentration and multiple elicitor applications. This IR model
is also extended to include a scenario of post-pathogen inoculation for elicitor treatment.
Finally, an application of optimal control theory is derived to determine the
best strategy for a continuous elicitor application. Numerical evaluations of this IR
model provide a potential support tool for the development of more potent elicitors
and its application strategies. The model is generic and will be applicable to a range
of plant-pathogen-elicitor scenarios.
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Keywords
Induced resistance, Plant resistance, Plant diseases and pests, Plant defence genes, Mathematical models of plant resistance, Research Subject Categories::MATHEMATICS