Optimal control of anthracnose using mixed strategies

TL;DR

This paper develops a spatial diffusion model for controlling anthracnose disease, analyzing continuous and discrete control strategies, proving well-posedness, and identifying optimal controls through numerical simulations.

Contribution

It introduces a generalized spatial diffusion model for anthracnose control, incorporating mixed control strategies and establishing existence, uniqueness, and optimality of solutions.

Findings

Optimal control strategies minimize disease spread.

Numerical simulations compare spatially averaged and full models.

Pulse and continuous controls can be effectively combined.

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 spatially averaged version of the model and for the full model.