Feedback stabilisation of a sterile insect control system: Applications to mosquito-borne disease control

par Kala Agbo

vendredi 3 oct. 2025, 11:00 → 11:30 Europe/Paris

XR203 (XLIM)

he sterile insect technique (SIT) has recently become one of the methods used for controlling mosquito populations. This technique involves the release of sterile mosquitoes that compete with wild males for mating with females. The mathematical study of this control system aims to develop strategies that optimize the release of sterile insects, stabilize  the population to zero, and prevent resurgence. 

The challenge of stabilizing the system to zero lies in the fact that, as the population approaches zero, fewer releases are needed to maintain the population close to zero asymptotically. However, sufficient sterile insects

must still be released to counteract, in particular, disturbances in the dynamic parameters. In control theory, many tools exist to address this problem, but they often fail to ensure the positivity of the control function. In this work, we apply the backstepping method to design a nonnegative feedback control law that addresses the problem of robustness and global asymptotic stability of the dynamics to zero. Additionally, we study other linear feedback control laws that can globally stabilize the control system. However, implementing these feedback control laws requires measuring the system states. We address this issue by designing an observer that, based on measurements of sterile and wild male mosquitoes, enables the estimation of the other components of the state of the system.

The implementation of SIT for controlling mosquito populations in practical situations also requires considering the spatial dispersion of adult mosquitoes.  Recent advance in using drones to release sterile male mosquitoes have improved the precision of the release, which helps improve their dispersion.

In our study, we consider a system of reaction-diffusion equations that models the spatial dispersion of mosquito populations in a two-dimensional bounded and smooth domain. We study sterile male releases within this framework. Under Neumann boundary conditions and assuming the same diffusion coefficient for sterile and wild males, we design nonnegative feedback laws which globally asymptotically stabilize the population to zero over the entire domain.