Abstract
In this paper, we propose a mosquito population suppression model which is composed of two sub-models switching each other. We assume that the releases of sterile mosquitoes are periodic and impulsive, only sexually active sterile mosquitoes play a role in the mosquito population suppression process, and the survival probability is density-dependent. For the release waiting period T and the release amount c, we find three thresholds denoted by T^*, g^*, and c^* with c^*>g^*. We show that the origin is a globally or locally asymptotically stable equilibrium when cge c^* and Tle T^*, or cin (g^*, c^*) and T<T^*. We prove that the model generates a unique globally asymptotically stable T-periodic solution when either cin (g^*, c^*) and T=T^*, or c>g^* and T>T^*. Two numerical examples are provided to illustrate our theoretical results.
Highlights
To prevent and control the spread of mosquito-borne diseases such as malaria, dengue fever and Zika, effective and biologically safe approaches are to suppress the wild mosquito populations by using the sterile insect technique (SIT), the genetic approaches, and the Wolbachia-driven mosquito control technique, in which sterile mosquitoes, including irradiated and Wolbachia-infected male mosquitoes, are released into the wild to mate with wild female mosquitoes [1,2,3,4,5,6]
In [29], the author supposed that the release function g of sterile mosquitoes is an independent variable satisfying an independent dynamical equation, see [1,32]
We have found the corresponding threshold values such as T ∗ for the waiting period between two consecutive releases, g∗ and c∗ for the release amount of the sterile mosquitoes each time
Summary
To prevent and control the spread of mosquito-borne diseases such as malaria, dengue fever and Zika, effective and biologically safe approaches are to suppress the wild mosquito populations by using the sterile insect technique (SIT), the genetic approaches, and the Wolbachia-driven mosquito control technique, in which sterile mosquitoes, including irradiated and Wolbachia-infected male mosquitoes, are released into the wild to mate with wild female mosquitoes [1,2,3,4,5,6]. Since the only function of the released males is to sterilize wild mosquitoes, only those sexually active sterile mosquitoes may play a role in the suppression process of wild mosquitoes Based on these observations, the author in [17] first gave a novel modeling idea by treating the number of sterile mosquitoes as a given function instead of an independent variable satisfying a dynamical equation to explore the interactive dynamics of wild and sterile mosquitoes. We investigate the existence, uniqueness and stability of T -periodic solutions to model (1.4)–(1.5) by using Poincaré map method These results may be helpful for optimal control of mosquito vector or mosquito-borne diseases as shown in [34].
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