Conceptual and mathematical modeling of insect-borne plant diseases: theory and application to flavescence doree in grapevine

Insect-borne plant diseases recur commonly in wild plants and in agricultural crops, and are responsible for severe losses in terms of produce yield and monetary return. Mathematical models of insect-borne plant diseases are therefore an essential tool to help predicting the progression of an epidemic disease and aid in decision making when control strategies are to be implemented in the field. While retaining a generalized applicability of the proposed model to plant epidemics vectored by insects, we specifically investigated the epidemics of Flavescence dor\'ee phytoplasma (FD) in grapevine plant Vitis vinifera specifically transmitted by the leafhopper Scaphoideus titanus. The epidemiological model accounted for life-cycle stage of S. titanus, FD pathogen cycle within S. titanus and V. vinifera, vineyard setting, and agronomic practices. The model was comprehensively tested against biological S. titanus life cycle and FD epidemics data collected in various research sites in Piemonte, Italy, over multiple years. The work presented here represents a unique suite of governing equations tested on existing independent data and sets the basis for further modelling advances and possible applications to investigate effectiveness of real-case epidemics control strategies and scenarios.