Modelling induced resistance to plant diseases

Plant disease control has traditionally relied heavily on the use of agrochemicals despite their potentially negative impact on the environment. An alternative strategy is that of induced resistance (IR). However, while IR has proven effective in controlled environments, it has shown variable field efficacy, thus raising questions about its potential for disease management in a given crop. Mathematical modelling of IR assists researchers with understanding the dynamics of the phenomenon in a given plant cohort against a selected disease-causing pathogen. Here, a prototype mathematical model of IR promoted by a chemical elicitor is proposed and analysed. Standard epidemiological models describe that, under appropriate environmental conditions, Susceptible plants (S) may become Diseased (D) upon exposure to a compatible pathogen or are able to Resist the infection (R) via basal host defence mechanisms. The application of an elicitor enhances the basal defence response thereby affecting the relative proportion of plants in each of the S, R and D compartments. IR is a transient response and is modelled using reversible processes to describe the temporal evolution of the compartments. Over time, plants can move between these compartments. For example, a plant in the R-compartment can move into the S-compartment and can then become diseased. Once in the D-compartment, however, it is assumed that there is no recovery. The terms in the equations are identified using established principles governing disease transmission and this introduces parameters which are determined by matching data to the model using computer-based algorithms. These then give the best match of the model with experimental data. The model predicts the relative proportion of plants in each compartment and quantitatively estimates elicitor effectiveness. An illustrative case study will be given; however, the model is generic and will be applicable for a range of plant-pathogen-elicitor scenarios.