数学一级学科Seminar 682
题目： 流行性传播中的数学建模的研究现况简介
报告人：宋宝军 副教授(Montclair State University, USA)
时间：2013年5月10日（周五)15:30
地点：校本部G507
主办部门：理学院数学系

ABSTRACT

        First, we will give a review of mathematical modeling on infectious disease spreading. I will introduce the methods, theories and current situation about the mathematics modeling about infectious disease spreading.
        Second, as an example, we are concerned with the persistence of curable transmission diseases such as gonorrhea. Persistence is the result of a combination of numerous reasons, where the lack of a proper treatment strategy at the population level might have played a role. A set of deterministic SIS models with density-dependent treatments are studied in understanding the disease dynamics when different treatment  trategies are applied. It is shown that when a backward bifurcation occurs, bi-stability appears. However, this study finds that when epidemic models undergo a backward bifurcation, different modes of bi-stability appear or may not happen at all. Specifically, it could be either the coexistence of two stable equilibria or the  oexistence of the disease-free equilibrium and a stable limit cycle. In addition, bi-stability may not be an option at all; the disease-free equilibrium could actually be globally stable. We also extend the mean infection period from  density-independent treatments to density-dependent ones. Finally, applying our results to the transmission of gonorrhea  in China, we conclude that Chinese gonorrhea patients may not seek medical treatments in a timely manner.