Assessing the effects of vector control on dengue transmission q Hyun Mo Yang a,1 , Cla ´udia Pio Ferreira b, * ,2 a UNICAMP – IMECC, Departamento de Matema ´ tica Aplicada, Caixa Postal 6065, CEP: 13081-970, Campinas, SP, Brazil b UNESP – IBB, Departamento de Bioestatı ´stica, Caixa Postal 510, CEP: 18618-000, Botucatu, SP, Brazil Abstract The dengue virus is an arbovirus transmitted to humans through mosquito Aedes aegypti. To describe the dynamics of dengue disease within these two populations we develop a compartment model taking into account chemical controls and mechanical control applied on the mosquitoes, which are the currently available controlling mechanisms to prevent dengue disease. To mimic seasonal variations, some parameters of the model are allowed to depend on time in order to divide a calendar year in favorable and unfavorable periods regarded to the development of vector population. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Mathematical modelling; Dengue transmission; Mosquito dynamics; Control strategies; Control efficacies 1. Introduction The dengue virus, a flavivirus transmitted by arthropod of the genus Aedes, is prevalent in different parts of the world, presents only one epidemiological cycle (urban) which comprises the human (host) and the mos- quito Aedes aegypti (vector). As a result of being pathogenic for humans and capable of transmission in heav- ily populated areas, dengue virus (arbovirus) can cause widespread and serious epidemics, which constitute major public health problems in many tropical and subtropical regions of the world where A. aegypti and other appropriate mosquito vectors are present [1]. There are four different serotypes of dengue virus presenting low cross immunity among them, which can result in secondary infections after an infection with one serotype had been occurred. It is known that an individual infected with one serotype can be infected with other serotype six months later the first exposure, but there is not evidence of reinfection with the same serotype. Dengue viruses of all four serotypes cause three distinct syndromes: classic dengue fever, dengue hemorrhagic fever and dengue shock syndrome. Although caused by the same viruses, dengue and dengue hemorrhagic fever are pathogenically, clinically 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.08.046 q Grant FAPESP (Polı ´ticas Pu ´ blicas and Tema ´tico) and CNPq (Edital Universal). * Corresponding author. E-mail address: pio@ibb.unesp.br (C.P. Ferreira). 1 Fellowship awarded by CNPq. 2 Fellowship awarded by FAPESP. Available online at www.sciencedirect.com Applied Mathematics and Computation 198 (2008) 401–413 www.elsevier.com/locate/amc