Population dynamics of disease-transmitting mosquitoes exposed to insecticides: susceptible and resistant interaction

Abstract

One of the first biological topics that have attracted physicists’ attention is population dynamics. Researchers have approached these topics through dynamical systems, which have its origin in 15th-century physics, with the invention of Newton’s differential equations. In particular, we are interested in studying mosquitoes transmitting diseases such as Anopheles, Aedes and Culex as they cause serious public health problems worldwide. One of the strategies to control these diseases has been the use of insecticides. These spraying programs were initially successful. However, the evolution of resistance threatens efforts to control these epidemics. Therefore, this article proposes a dynamic system that includes continued use of an insecticide, assuming a proportion of mosquitoes not killed by spraying but acquire resistance. In addition, the genetic predisposition of mosquitoes to be more susceptible or more resistant is incorporated in the model utilizing a ratio that allows differentiating mosquitoes that are born susceptible from those that are born resistant. The dynamic system analysis shows that population persistence depends on growth thresholds that depend on resistance parameters. Therefore, according to the model, to avoid epidemics caused by mosquitoes, the emergence of resistant mosquito populations must be prevented.