Speaker: Kevin Church

Institution: University of Waterloo

Title: Control of malaria in the presence of insecticide-resistant mosquitoes

Abstract: Surveillance data is a hugely important tool in the design and implementation of public health policy and strategies. In regions of the world where malaria is endemic, there is a need to understand how such data can inform malaria control policies. Indeed, the World Health Organization has identified effective surveillance as a critical component in malaria elimination and has called for stronger surveillance systems to track and prevent outbreaks in endemic regions.

Vector control methods – that is, methods that control the mosquito population responsible for spreading the disease to humans – have been highly effective at reducing prevalence in endemic areas. However, there is evidence of resistance to the more insecticide-based control measures currently in use. In this presentation, we will introduce and analyze a compartmental model of malaria transmission that features an impulsive insecticide control as well as a mutant strain of mosquito that is resistant to the insecticide. The control is applied at times that are determined by passive surveillance data.

While the model is eight-dimensional, the dynamics pertaining to the insecticide control and the resistant strain of mosquitoes can be understood by considering a two-dimensional submodel. This submodel, while seemingly simple, can exhibit a wealth of interesting dynamical phenomena. We present a brief introduction to bifurcation theory of impulsive systems and demonstrate how the theory can be used to determine safe control guidelines to limit the growth of the mutant strain.