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 $s_g^{\ast }$ 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 $s_g^{\ast }$. 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 $s_g^{\ast }$.

摘要

在这项工作中，我们研究了野生和无菌蚊子相互作用的非自治微分方程模型。假设在现场释放的无菌蚊子的数量是给定的非负连续函数。我们确定一个阈值$s_G^{\ast }$ 消毒蚊子的数量，并为起源提供足够的条件 $s_0$ 基于阈值是全局渐近稳定的 $s_G^{\ast }$。对于无菌蚊子数量保持恒定的情况，我们发现$s_0$ 当且仅当常数为常数时，它是全局渐近稳定的 $s_G$ 上面释放的无菌蚊子数量以上 $s_G^{\ast }$。