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Optimal control of plant virus propagation
Author(s) -
ChenCharpentier Benito,
Jackson Mark
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6244
Subject(s) - optimal control , predation , population , ordinary differential equation , mathematics , mathematical optimization , function (biology) , limit (mathematics) , ecology , differential equation , biology , mathematical analysis , demography , evolutionary biology , sociology
Plants are a food source for man and many species. But, plants are subject to diseases, many of which are caused by viruses. Usually, virus propagation is done by a vector. Insect vectors typically have a seasonal behavior, and processes have delays. To combat the vectors, chemical insecticides are commonly used as a control. Unfortunately, these chemicals not only are expensive but also have toxic effects on humans, animals, and the environment. An alternative is to introduce a predator species to prey on the insects and limit the spread of the virus. A combination of insecticide and predators can be used to control the vector population. The question is whether there is an optimal combination. We introduce a mathematical model of ordinary differential equations describing the interaction between plants, vectors, and predators. To determine the optimal amount of predators to introduce and insecticide to use, an objective function giving the total cost to the farmer of the disease is given. We find the controls that minimize the objective function subject to the population variables satisfying the differential equation model and initial conditions together with constraints. There are two main different approaches that can be used to solve the optimal control problem: indirect and direct methods. We use direct methods to solve the problem with and without seasonality and delays. From the practical side, the model can be used to help farmers determine the right balance of insecticide and predators to minimize the total cost.

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