Finite-Time Contraction Stability and Optimal Control for Mosquito Population Suppression Model

Abstract

Releasing Wolbachia-infected mosquitoes into the wild to suppress wild mosquito populations is an effective method for mosquito control. This paper investigates the finite-time contraction stability and optimal control problem of a mosquito population suppression model with different release strategies. By taking into account the average duration of one reproductive cycle and the influences of environmental fluctuations on mosquitoes, we consider two cases: one with a time delay and another perturbed by stochastic noises. By employing Lyapunov’s method and comparison theorem, the finite-time contraction stabilities of these two cases under a constant release strategy are analyzed. Sufficient conditions dependent on delay and noise for these two systems are provided, respectively. These conditions are related to the prespecified bounds in finite-time stability (FTS) and finite-time contraction stability (FTCS) of the system, and FTCS required stronger conditions than FTS. This also suggests that the specified bounds and the delay (or the noise intensity) play a critical role in the FTCS analysis. And finally, the optimal control for the stochastic mosquito population model under proportional releases is researched.

Keywords

• <i>Wolbachia</i>-infected mosquitoes
• finite-time contraction stability
• optimal control
• time delay
• stochastic noises