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.

巴西最大的柑橘产区，集中在圣保罗州和米纳斯吉拉斯州，也是世界上最大的柑橘产区。2016 年的数据表明，世界上每消费 5 杯橙汁，就有 3 杯产自巴西。因此，柑橘栽培在巴西农业综合企业中脱颖而出。随着这一农业部门的发展，柑橘树病害的出现也随之而来。在本文中，提出了两个数学模型来描述柑橘病害的动力学和化学防治。这些模型涉及最优控制理论，考虑到疾病媒介的空间传播。第一个模型由具有传输速率的常微分方程组组成。第二个模型涉及控制理论中的贪婪随机自适应搜索过程，考虑来自涉及扩散的偏微分方程模型的向量的传播。这些模型是在黄龙病（也称为绿化）的情况下进行的，由于其特征和它造成的损害，并且仍然无法治愈，黄龙病被认为是世界上最具破坏性的柑橘病害。