Stephen Gourley (University of Surrey)

Modelling the evolution of insecticide resistance in mosquitoes and effective use of insecticides

A big problem in malaria control is the rapidity with which mosquitoes can develop resistance to insecticides. The possibility of creating evolution-proof insecticides is therefore of considerable interest. Biologists have suggested that effective malaria control, with only weak selection for insecticide resistance, could be achieved if insecticides target only old mosquitoes that have already laid most of their eggs. The strategy aims to exploit the fact that most malarial mosquitoes do not live long enough to transmit the disease. In this talk two mathematical models will be derived, analyzed and compared, one for an insecticide that kills on exposure, and the other for an insecticide that targets only older mosquitoes. Both models predict that insecticide-resistant mosquitoes will become dominant over time but, very importantly, this occurs on a very much slower time scale when the insecticide only affects older mosquitoes. Analytical results will be presented on linear and global stability of the nontrivial equilibrium in which only the resistant mosquito strain is present, together with a theorem comparing the rates of convergence for the two models. Numerical simulations show that the effect of targeting only old mosquitoes on the evolution of resistance is dramatic. This is joint work with Rongsong Liu and Jianhong Wu.