| Malaria、dengue fever and other mosquito-born diseases are transmitted by mosquitoes.To prevent the transmissions of mosquito-borne diseases,one of effective weapons is to reduce or eradicate the wild mosquitoes.In recent years,the sterile insect technique has been applied to the practical method.We establish and study two types transmission dynamic models of releasing sterile mosquitoes in this paper.One transmission dynamic model focuses on the mosquito population affected by the Allee effect.The other mosquito population transmission dynamic model incorporate the factor of climate.Specifically,based on the Allee effect and the number of the wild mosquitoes is varying,we firstly formulate three different dynamic models where the releasing rate of sterile mosquitoes is constant,proportional and Holling-II.Using the stability theory and method of differential equations,then gaining the threshold value of releasing sterile mosquitoes.In the meantime,we analyze the existence of equilibria and stability of the equilibria of the system when the amount of sterile mosquitoes advertising is different with the threshold release value,obtaining the optimal delivery strategy of the system.Secondly,according to the characteristics of the mosquito population in the influence of climate.We establish the mosquito population transmission dynamic model with the climate and releasing sterile mosquitoes.Using the topological degree theory and comparison theorem of differential equations,getting the existence of the periodic solutions of the system.We finally study the impact of different releasing strategies and provid the economical and effective methods for controlling the amount of mosquito population. |
