  In this paper we propose and study a spatial diffusion model for the control
of anthracnose disease in a bounded domain. The model is a generalization of
the one previously developed in [14]. We use the model to simulate two
different types of control strategies against anthracnose disease. Strategies
that employ chemical fungicides are modeled using a continuous control
function; while strategies that rely on cultivational practices (such as
pruning and removal of mummified fruits) are modeled with a control function
which is discrete in time (though not in space). Under weak smoothness
conditions on parameters we demonstrate the well-posedness of the model by
verifying existence and uniqueness of the solution for given initial
conditions. We also show that the set [0; 1] is positively invariant. We first
study control by pulse strategy only, then analyze the simultaneous use of
continuous and pulse strategies. In each case we specify a cost functional to
be minimized, and we demonstrate the existence of optimal control strategies
that can be evaluated numerically using the gradient method presented in [1].
We discuss the results of numerical simulations both for a spatially averaged
version of the model and for the full model.
