Modelling malaria control by introduction of larvivorous fish

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host-vector interaction and the predator-prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.