Backstepping control for the sterile mosquitoes technique: stabilization of extinction equilibrium
Andrea Cristofaro, Luca Rossi
TL;DR
The paper addresses extinction stabilization of a mosquito population controlled by sterile insect releases. It develops a backstepping control design on a reduced two-state model $(F,M_s)$ with dynamics $\dot{F}=g(F,M_s)-\delta_F F$ and $\dot{M_s}=u-\delta_s M_s$, constructing a virtual control $M_s^*(F)$ and a feedback $u^\star(F,M_s)$ that yields global positive exponential convergence to $(0,0)$, with a rate $\lambda=2\min\{\delta_F-\epsilon,\eta\}$. A nonnegative variant $u_+^\star$ ensures physical feasibility ($u\ge0$) while maintaining stability, and a saturated/modified form $\tilde{u}^\star$ extends the result globally. Simulations show successful stabilization for both the reduced and complete models, and robustness checks under parameter uncertainty indicate the approach is resilient and practically viable for SIT-based population suppression.
Abstract
The control of a mosquito population using the sterile insect technique is considered. Building on a model-based approach, where the control input is the release rate of sterilized males, we propose a non-negative backstepping control law capable of globally stabilizing the extinction equilibrium of the system. A simulation study supports and validates the theoretical findings, showing the efficacy of the approach both on a reduced model, used for control design, and on a complete model of the mosquito population dynamics.