Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito

• We consider a delayed model for the control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT).
• The existence of positive equilibria is characterized in terms of two biologically relevant threshold quantities.
• A nonstandard finite difference (NSFD) scheme is used to approximate the continuous model.
• It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures, the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures.

This paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the “richer” equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase.A nonstandard finite difference (NSFD) scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model. The resulting discrete model is transformed into a delay-free model by using the method of augmented states, a necessary condition for the existence of optimal controls then determined. The particularities of different control regimes under varying environmental temperature are investigated by means of numerical simulations. It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures, the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures.