Lecturer: Yu Jianshe

Abstract:Based on the idea that only those sexually active sterile mosquitoes are included in the modeling process, we study the dynamics of the interactive wild and sterile mosquito model with time delay, which consists of three subequations. Due to the fact that the maturation period of sterile mosquitoes bred in the lab or mosquito factories is the same time period of wild adults mature from larvae, we particularly assume that the waiting period for two consecutive releases of sterile mosquitoes equals the maturation period of wild mosquitoes, as a new practical sterile mosquito release strategy. We first ingeniously solve the delay model with the initial functions that are solutions of the corresponding equation without delay, referred to as “good” solutions. Using these “good” solutions, we then surprisingly obtain sufficient and necessary conditions for the trivial solution and a unique periodic solution of the delay model to be globally asymptotically stable, respectively. We provide a numerical example to demonstrate the model dynamics and brief discussions of our findings as well.

We are confident that the results obtained and the methods used in this paper can be applied to other similar situations where no existing results and methods are available.

Introduction to the Lecturer:Yu Jianshe is a professor, doctoral tutor, winner of the National Science Fund for Distinguished Young Scholars, young and middle-aged expert with outstanding national contributions, candidate at the first and second levels of the Hundred-Thousand-Ten Thousand Talents Project, cross-century talent of the Ministry of Dducation, director of the Applied Mathematics Research Center of Guangzhou University, and member of the Standing Committee of the Director Committee of the International Society of Difference Equations. He is mainly engaged in the theory and application research of differential equation dynamic system, difference equation and biological mathematical model. He has successively presided over more than 10 projects of National Natural Science Foundation of China, including 3 key projects and 2 mathematical cross research platform projects. He has won one first prize for national teaching achievements and four first prizes for provincial and ministerial scientific and technological achievements and teaching achievements, and has published many papers in important international journals of mathematics and applied mathematics such asNATURE,PloS Comput. Biol.andJ. Differential Equations.

Invitee:Si Jianguo, Professor from School of Mathematics

Time:14:00-15:00, October 15 (Friday)

Venue:Tencent Meeting ID: 568 268 679

Hosted by the School of Mathematics, Shandong University