### A Multiobjective Optimization Application to Control the Aedes Aegypti Mosquito using a Two-Dimensional Diffusion-Reaction Model

#### Abstract

Aedes aegypti is the main vector of multiple diseases, such as dengue, yellow fever, Zika, and chikungunya. Diseases associated with mosquitoes have been growing in recent years, with more than one-third of the world population at risk. Control techniques have been studied to prevent the spread of the Aedes aegypti, such that new formula and how to use adulticides and larvicides, among others. This paper proposes a novel approach in the field of partial differential equations and optimization. We consider a two-dimensional diffusion-reaction model that describes the interaction between aquatic and adult female stages spreading across a domain with parameters dependent on rainfall and temperature. We also formulate a mono-objective and multiobjective optimization problem to minimize the Aedes aegypti populations and the control, considering the application of adulticides and larvicides, using actual data from the city of Lavras/Brazil. The operator splitting technique is used to solve the diffusion-reaction system, coupling finite difference and the fourth-order Runge-Kutta method and optimal solutions were searched by using the Real-Biased Genetic Algorithm and Non-dominated Sorting Genetic Algorithm -II. Numerical results show significant reduction of the Aedes aegypti population.

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DOI: https://doi.org/10.5540/tcam.2023.024.04.00779

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