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

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.