Optimal Control of Aedes Aegypti Mosquitoes by Sterile Insect Technique, Insecticide and Larvicide

Roberto Carlos Antunes Thomé¹; Claudia Mazza Dias²; Edilson Fernandes Arruda³; Dayse Haime Pastore¹; Hyun Mo Yang⁴

¹ Centro Federal de Educação Tecnológica Celso Suckow da Fonseca; ² Universidade Federal Rural do Rio de Janeiro; ³ Universidade Federal do Rio de Janeiro; ⁴ Universidade Estadual de Campinas

doi:10.20906/CPS/CILAMCE2015-0072

Resumo

The work presents a model to describe the dynamics of Aedes aegypti mosquitoes population when sterile individuals are introduced as a biological control, besides the application of insecticide and larvicide. In order to analyse the minimal effort to reduce the female mosquitoes, which are responsable to the spread of diseases like dengue and chikungunya fever, an optimal control strategy is used considering the cost of the insecticide and the larvicide application, the cost of the production of sterile mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized female mosquitoes). The optimal control is obtained by applying the Pontryagin's maximum principle.

Palavras-chave: Optimal Control; Mathematical Modelling; Pontryagin's Maximum Principle; Aedes Aegypti