Session S15 - Mathematics of Planet Earth

Tuesday, July 20, 16:00 ~ 16:25 UTC-3

Control strategies for a population dynamics model of Aedes aegypti with seasonal variability and their effects on dengue incidence and some ideas on estimating regional carrying capacity from the study of mathematical models that allow quantifying the productivity of mosquito breeding sites.

Andres Fraguela Collar

Benemerita Universidad Autonoma de Puebla, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Aedes aegypti female mosquitoes are the principal transmitters of dengue and other vector borne infections. This species is closely associated with human habitation, due to its blood-feeding habits and the presence of breeding sites widely available around house holds. We introduce a mathematical model for the life cycle of Aedes aegypti mosquitoes comprising two stages, aerial and aquatic, that reflects seasonal changes in the mosquito abundance. This model is further amended by three season-dependent control actions. Two coercive actions are introduced during the hot seasons characterized by higher abundance and enhanced growth rates of mosquitoes. They consist in the application of two chemical substances, insecticide and larvicide, acting upon the aerial and aquatic mosquito stages, respectively. During the cool seasons, characterized by the slower growth rates of mosquitoes and abundance of quiescent unhatched eggs, we introduce a preventive vector control measure consisting in mechanical elimination of mosquito breed ing sites. Using the framework of optimal control in combination with the cost-benefit ap proach and epidemiological assessment, we identify the most efficient strategy capable of essentially reducing the population of adult and immature mosquitoes during both seasons and provide a sketch for its modus operandi. For the study of the control problem it is very important to be able to obtain reliable estimates of the regional carrying capacity. For this reason, we will end by announcing some ideas on how we are studying this problem by introducing models of the evolution of the mosquito in the aquatic state that allow us to reasonably quantify the productivity of the hatcheries.

Joint work with Emilene Pliego Pliego (Benemerita Universidad Autonoma de Puebla, Mexico),, Tishbe Pilar Herrera Ramírez (Benemerita Universidad Autonoma de Puebla, Mexico),, Jorge Velázquez Castro (Benemerita Universidad Autonoma de Puebla, Mexico),, Olga Vasilieva (Universidad del Valle, Colombia) and Antonio Abella Medrano (Universidad Nacional Autónoma de México).

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