Mating versus alternative blood sources as determinants to mosquito abundance and population resilience

A deterministic nonlinear ordinary differential equation model for mosquito dynamics in which the mosquitoes can quest for blood either within a human population or within non-human/vertebrate populations is derived and studied. The model captures both the mosquito's aquatic and terrestrial forms and includes a mechanism to investigate the impact of mating on mosquito dynamics. The model uses a restricted form of homogeneous mixing based on the idea that the mosquito has a blood-feeding habit determined by its blood-feeding preferences and its gonotrophic cycle. This characterisation allows us to compartmentalise the total mosquito population into distinct compartments according to the spatial location of the mosquito (breeding site, resting places and questing places) as well as blood-fed status. Issues of overcrowding and intraspecific competition both within the aquatic and the terrestrial stages of the mosquito's life forms are addressed and considered in the model. Results show that the inclusion of mating induces bistability, a phenomenon whereby locally stable trivial and non-trivial equilibria co-exist with an unstable non-zero equilibrium. The local nature of the stable equilibria is demonstrated by numerically showing that the long-term state of the system is sensitive to initial conditions. The bistability state is analogous to the phenomenon of the Allee effect that has been reported in population biology. The model's results, including the derivation of the threshold parameter of the system, are comprehensively tested via numerical simulations. The output of our model has direct application to mosquito control strategies, for it clearly shows key points in the mosquito's developmental pathway that can be targeted for control purposes.