Academic Report of School of Mathematical Sciences [2026] No. 029

(Series Report for High-Level University Construction No. 1288)

Title：Target reproduction numbers for time-delayed population systems

Speaker：Xueying Wang, Professor (Washington State University)

Time：9:30-10:30, Apr. 8, 2026

Location：Huixing Building 514

Abstract：In the field of population dynamics, target reproduction number is a crucial metric that dictates the necessary control efforts for achieving specific prevention, intervention, or control goals. Recently, the concept of the target reproduction number has undergone significant extensions. Lewis et al. (JMB, 2019)presented a general framework of the target reproduction number for nonnegative matrices, and Wang and Zhao (JMB, 2020) further developed it to positive operators on an ordered Banach space. These extensions encompass fundamental metrics like basic reproduction number and type reproduction number, along with other threshold parameters from existing literature, elucidating their roles in population control. In the current paper, we establish the theory of target reproduction number for a large class of compartmental population models with time delay in the case where control is targeted toward either new infection/production or internal evolution/transition. It turns out that the target reproduction number of the original time-delayed population model can be viewed as a basic reproduction number of some modified system. At the end, we apply these analytic results to three epidemic models, which enhances our theoretical understanding and provides valuable insights for effective strategies in population-based interventions and control measures.

Speaker Profile：Dr.Xueying Wang is a professor in the Department of Mathematics and Statistics at Washington State University whose work focuses on mathematical modeling in biology, including infectious and neuroscience.

Faculty and students are welcome to attend!

Invited by: Pei Yuan

School of Mathematical Sciences

April 7, 2026