Optimal control of anthracnose using mixed strategies

Abstract

Abstract-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 spatiallyaveraged version of the model and for the full model.