Mathematical modelling and optimal control of anthracnose

TL;DR

This paper develops and analyzes nonlinear mathematical models, including spatial diffusion, for controlling anthracnose disease, and derives optimal control strategies with theoretical and numerical validation.

Contribution

Introduces two nonlinear models for anthracnose control, including a spatial diffusion component, and derives optimal control strategies with theoretical proofs and numerical simulations.

Findings

Existence of solutions for the models is established.

Optimal control strategies are characterized and numerically evaluated.

Models provide a framework for effective disease management.

Abstract

In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the well-posedness of those models by verifying the existence of solutions for given initial conditions and positive invariance of the positive cone. By considering a quadratic cost functional and applying a maximum principle, we construct a feedback optimal control for the ODE model which is evaluated through numerical simulations with the scientific software Scilab. For the diffusion model we establish under some conditions the existence of an optimal control with respect to a generalized version of the cost functional mentioned above. We also provide a characterization for this optimal control.