title: Modelling and analysis of impulsive releases of sterile mosquitoes.
abstract: To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.
authors.affiliation: a College of Mathematics and information Science , Xinyang Normal University , Xinyang , Henan , People's Republic of China.|b Research Institute of Forest Resource Information Techniques , Chinese Academy of Forestry , Beijing , People's Republic of China.
authors.forename: Mingzhan
authors.initials: M
authors.lastname: Huang
authors.affiliation: a College of Mathematics and information Science , Xinyang Normal University , Xinyang , Henan , People's Republic of China.
authors.forename: Xinyu
authors.initials: X
authors.lastname: Song
authors.affiliation: c Department of Mathematical Sciences , University of Alabama in Huntsville , Huntsville , AL , USA.
authors.forename: Jia
authors.initials: J
authors.lastname: Li
mesh_terms: D000818:Animals; D009033:Culicidae / Q000502:physiology*; D007246:Infertility; D008954:Models, Biological; D009032:Mosquito Control; D000072138:Mosquito Vectors / Q000502:physiology
keywords: 4D20; 92D25; 92D30; 92D40; Sterile mosquitoes; impulsive release; periodic solution; semi-continuous dynamical system