Establishing the Coexistence of Wolbachia-Carrying and Wild Aedes aegypti Populations by Feedback Linearization

Wolbachia-based control for the reduction of arboviruses transmitted by Aedes aegypti mosquito is often designed to thoroughly wipe out the wild population replacing it by Wolbachia-carrying individuals. Overall, there has been no focus on plans looking for establishing the coexistence of these populations sharing the same locality. Holding repeated replacement interventions could lead us in a long-term to a possible eradication scenario for this species in its natural state. Nevertheless, annihilating species has been a subject of great controversy and qualms among conservative scientists, since there is no warranty of safeguarding the ecological balance and human welfare. Taking this into account, we explore the application of two non-classical techniques for optimal control proposition, Feedback (Exact) Linearization and Genetic Algorithm, to a system composed of Wolbachia-carrying and wild Aedes aegypti populations aiming to achieve the coexistence equilibrium. The Feedback Linearization technique is used to provide a control law by which one rules the releases of Wolbachia-carrying mosquitoes so that the system solution locally asymptotically stabilizes around the coexistence steady-state. In addition, the Genetic Algorithm is used to propose a control strategy to be introduced in a worst-case scenario, when the wild population is at the level of the carrying-capacity without the presence of Wolbachia-carrying mosquitoes. Remarkably, the presented strategy is very interesting because it consists in applying the control with higher intensity in the early days and fairly low as the solution approaches the coexistence equilibrium. Furthermore, the control can be temporarily interrupted, reducing the costs to zero for a considerable length of time.