Global Dynamics of a Spore Producing Pathogens Epidemic System with Nonlocal Diffusion Process

In this paper, we analyze a nonlocal spatial epidemic model presenting the diffusion process of a spore producing plant pathogens responsible of one of the most destructive cocoa pods disease. The global existence, compactness and dissipativity of the semiflow generated by the system are established. By defining a threshold number (the basic reproduction number), we first express conditions for the existence of non-trivial stationary states. Next, we show that the qualitative dynamics of the model range from the extinction (i.e. the global stability of the disease-free stationary state), to the persistence (i.e. the global stability of the endemic stationary state) of the epidemics. Finally, we go through some simulations of our general analysis.