Consequences of insecticides on the dynamics of Anopheles mosquitoes

Abstract

Physics is a science that has developed valuable contributions to the understanding of different phenomena; in particular, the concept of a dynamic system originates in Newtonian mechanics; a concept that allows predictions of phenomena that are changing over time. The evolution rule is an implicit relation that can be given by a differential equation; our goal is to use dynamic systems in a problem of global importance, such as malaria. This is a potentially fatal disease caused by parasites transmitted to humans by biting infected female mosquitoes of the genus Anopheles; control is mainly due to combating the vectors. However, extensive use of insecticides has subjected mosquitoes to intense selection pressure, resulting in the development of physiological and behavioural resistance; therefore, we propose to study the dynamics of resistant and non-resistant infected mosquitoes. Our contribution is a system of ordinary differential equations in which non-resistant mosquitoes are assumed to have a logistic growth and exit upon developing resistance. In addition, we assume that resistant mosquitoes can have non-resistant offspring and only natural death; we performed a stability analysis of the model, allowing us to conclude that both types of mosquitoes always exist beyond a certain threshold. In addition, we performed a numerical study considering different levels of insecticide represented by the deaths it produces.