A spatiotemporal SEIR model for predicting wheat stripe and leaf rusts epidemics

Understanding the dynamics and severity of foliar fungal diseases in space and time is crucial to ensure effective epidemic control. Here, we presented a Susceptible-Exposed-Infected-Removed (SEIR) modeling approach integrating a nonlocal dispersion model of wind-borne pathogens and meteorological factors to describe the dynamics of wheat stripe rust (WSR) and wheat leaf rust (WLR). Variations of wheat plant populations from one compartment to another were modeled with weather dependent probabilities based on defined assumptions for the host population and wind velocity. The well-posedness of the formulated model was established and the final size of the epidemic was theoretically determined. Data for the 2018/2019 wheat cropping season from four representative wheat-growing regions in Luxembourg were used to fit the SEIR model for each disease and evaluate its capability to simulate disease progress and severity. Numerical simulations were carried out to visually assess the spatiotemporal patterns of the $S$, $E$, $I$, and $R$ compartments over a two-dimensions computational domain during the period of May to July 2019, which corresponds to the critical period of WSR and WLR development at the study sites. The SEIR model was fitted using unmanned aerial vehicle (UAV) imagery data for both WSR and WLR, and overall, the results showed a good fit between the simulated disease severity and the UAV-derived estimates.