Stability analysis in a mosquito population suppression model

Abstract

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold $s^{*}_{g} $ for the number of sterile mosquitoes and provide a sufficient condition for the origin $s_0 $ to be globally asymptotically stable based on the threshold $s^{*}_{g} $. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin $s_0 $ is globally asymptotically stable if and only if the constant number $s_{g} $ of sterile mosquitoes released in the field is above $s^{*}_{g} $.

Keywords

• mosquito population suppression
• sterile mosquitoes
• mosquito-borne diseases
• non-autonomous differential equation
• global asymptotic stability
• bi-stability