Mathematical models for exploring insecticide resistance in vector mosquitoes

The emergence and spread of insecticide resistance compromises the control of mosquito borne diseases that are responsible for millions of deaths every year in tropical and subtropical areas. Mathematical modelling is a valuable tool that can be used to explore different aspects of the development and management of insecticide resistance. We have used standard population genetics theory and ecological modelling techniques for developing models to evaluate the spread of resistance in the field. We started by developing a methodology to quantify the strength of selection for resistance occurring in nature. We used data from Mexico on the mosquito Aedes aegypti and a maximum likelihood methodology to estimate the selection and dominance coefficients driving the evolution of resistance in the field. We additionally explored the impact of poor data collection, data that combine information from different locations, and the consequences of selection and dominance coefficients varying over the sampling time period. This analysis highlighted factors highly relevant to field work such as the need for frequent surveillance in discrete sentinel sites. The use of insecticidal bed nets represents the primary tool for the prevention of malaria worldwide. It is of extreme importance to maintain their efficacy against mosquitoes, which has been undermined by the development of insecticide resistance. We assed the contribution of a novel design of bed nets in delaying insecticide resistance while at the same time determining the important parameters in driving resistance in an heterogeneous environment. We showed that this new bed net can indeed contribute to the delay of the spread of resistance, but surprisingly could have the reverse effect in specific circumstances. Finally we developed a model for the vector of malaria, that considers the stage-structured nature of the mosquito life cycle and, most importantly, explicitly incorporates insecticide resistance. It can be used to understand the population dynamics of mosquitoes throughout their entire lifecycle while analysing the impact of vector control interventions, alone and in combination, and the spread of insecticide resistance that those interventions induce. We showed that targeting the larval stages has the greatest effect on the adult population followed by targeting non host-seeking female adults. According to our results, low levels of resistance can induce failure of interventions, and the rate of spread of resistance is faster when insecticides target the larval stages