Received: 15 April 2018 DOI: 10.1002/mma.5527 SPECIAL ISSUE PAPER Controlling Aedes aegypti populations by limited Wolbachia-based strategies in a seasonal environment Marat Rafikov 1 Magno Enrique Mendoza Meza 1 Diego Paolo Ferruzzo Correa 1 Ana Paula Wyse 2 1 Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas, Universidade Federal do ABC, Santo André, SP, Brazil 2 Centro de Informática, Universidade Federal da Paraíba, João Pessoa, PB, Brazil Correspondence Marat Rafikov, Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas, Universidade Federal do ABC, Av. dos Estados, 5001, Bairro Santa Terezinha, Santo André, SP, Brazil. Email: marat.rafikov@ufabc.edu.br Communicated by: J. Vigo-Aguiar Funding information Fundação de Amparo a Pesquisa do, São Paulo Research Foundation, Estado de São Paulo, Grant/Award Number: 2015/09363-4 MSC Classification: 92D25; 49J15 In this work, the linear feedback limited control strategy is proposed to indicate how the Wolbachia-infected mosquitoes should be introduced in the seasonal environment to reduce the non-Wolbachia mosquito population. The numerical simulations show that the proposed strategy reduces the population level of non-Wolbachia mosquitos, avoiding mosquito spread and, consequently, reduc- ing the number of cases of vector-borne diseases. KEYWORDS Aedes aegypti, mosquito populations, optimal control, Wolbachia 1 INTRODUCTION The Aedes aegypti mosquito is the primary vector of dengue and responsible for other three important arboviral diseases: zika, chikungunya, and yellow fever. 1-3 The impact caused by these diseases, because of high incidences, morbidity, and mortality as well as the wide geographic distribution of A. aegypti, make it one of the most studied mosquitoes in the literature. Arboviruses are transmitted to humans through bites of infected female mosquitoes. Isolated conventional strategies, such as chemicals and extermination of reproduction spots, have not significant effect on mosquito population control and, consequently, on the advance of epidemics. 4 Because of recent advances in threshold-dependent gene drives for mosquitoes, the contamination of A. aegypti mosquitoes by Wolbachia appears as a viable alternative to compose a set of actions whose goal is the eradication of diseases transmitted by this mosquito. Wolbachia is a bacterium that can live inside the cells of most of the arthropods establishing a symbiotic relationship with them. This endosymbiotic bacteria is able to inhibit viral replication in the mosquito 5 and to reduce its lifespan. 6 The field releases of the Wolbachia-infected mosquitoes in Cairns, Australia, as a biocontrol strategy indicate that virus blocking is likely to persist in Wolbachia-infected mosquitoes after their release and establishment in wild popula- tions, suggesting that Wolbachia biocontrol may be a successful strategy for reducing dengue transmission in the field. 7 Researches about the dynamics and spreading of A. aegypti infected by Wolbachia have been studied to better understand this relationship and evaluate the impact of the infection in mosquito. These studies result in complex systems represent- ing empiric mathematical models, based on a multidisciplinary approach, integrating specialized theoretical knowledge, computational, and field/laboratory experience. 8-13 Math Meth Appl Sci. 2019;1–10. wileyonlinelibrary.com/journal/mma © 2019 John Wiley & Sons, Ltd. 1