Optimal control of Aedes aegypti using rainfall and temperature data

• Published in: Computational & applied mathematics 2022-04, Vol.41 (3), Article 91
• Main Authors: Vasconcelos, Amália S. V., Lima, Josenildo S., Cardoso, Rodrigo T. N., Acebal, José L., Loaiza, Aníbal M.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Environmental management; Genetic algorithms; Infectious diseases; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical models; Mathematics; Mathematics and Statistics; Maximum principle; Mosquitoes; Optimal control; Parameter estimation; Rainfall; Runge-Kutta method; Stability analysis
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-022-01804-7

The Aedes aegypti mosquito is a vector of several world’s leading infectious diseases. Monitoring and environmental management techniques have been developed and improved to control mosquito infestation. A mathematical model with a dependence of the parameters on temperature and rainfall is used to represent the population of life-stages of the Aedes aegypti . The local and global stability of the model is analyzed. Field data from females mosquitoes captured by traps in the city of Lavras (Brazil) were considered to calibrate the model parameters for summer and spring data. Based on the Pontryagin Maximum Principle, an optimal control problem was formulated to evaluate costs in environmental management control actions using adulticides and larvicides. The model was solved numerically by the Runge–Kutta algorithm. The model parameters were estimated using a Real-Biased Genetic Algorithm, and the optimal control problem was obtained employing the Forward–Backward Sweep method. The findings indicate a reasonable adjustment of the field data and efficiency in reducing the Aedes aegypti population when using all the proposed control approaches. Furthermore, control in two seasons proved to be more effective in combating the vector than control in just one season.