A PARTIALLY DIFFUSIVE MODEL FOR FROGEYE LEAF SPOT EPIDEMICS IN SOYBEAN.

We propose a new mathematical model based on partial differential equations to study the dynamics of the soybean disease frogeye leaf spot, a major affliction caused by the fungus Cercospora sojina. Our model extends the ordinary differential equations framework developed in earlier studies to incorporate the spatial diffusion of the disease within soybean plants. We prove the global-in-time solution theory of the model, determine the basic reproduction number for the system, and analyze the long-time behavior of the system subject to different values of the basic reproduction number. Our proof consists of two major mathematical novelties. First, although the model includes multiple infection-related compartments governed by non-diffusive equations - specifically the exposed and infected plants - with interactions that are not purely damping, we are able to provide the rigorous definition of the basic reproduction number. Second, despite the presence of multiple non-diffusive nonlinear equations - particularly for the susceptible and exposed compartments - we are able to prove the minimum principle by taking advantage of the structure of our model. In addition, we employ numerical simulation to verify the analytical results, to demonstrate the utility of this modeling framework, and to provide further insights into the spread of the disease.