Optimal control in citrus diseases

Abstract

The largest citrus-producing region in Brazil, concentrated in the states of São Paulo and Minas Gerais, is also the largest citrus-producing region in the world. Data from 2016 indicate that for every five glasses of orange juice consumed in the world, three are produced in Brazil. Thus, citriculture stands out in Brazilian agribusiness. Along with the growth of this agricultural sector is the emergence of diseases that affect citrus trees. In this paper, two mathematical models are presented to describe the dynamics and chemical control of citrus diseases. These models involve the theory of optimal control, considering the spatial spread of disease vectors. The first model consists of a system of ordinary differential equations with transport rates. The second model involves the Greedy Randomized Adaptive Search Procedure in control theory, considering the spread of the vectors from a partial differential equation model involving diffusion. The models are approached in a scenario for Huanglongbing disease, also called greening, which is considered to be the most devastating citrus disease in the world because of its characteristics and the damage it causes, and because there is still no cure.