报告题目：Dynamics of Drug on-Drug off Models with mutations in Morbidostat

报告摘要：Morbidostat is a bacteria culture device that progressively increase antibiotic drug concentration. It is used to study the evolutionary pathway. In this talk we consider three cases, namely the morbidostat with forward mutations, with forward-backward mutations and with no mutations. We study the case of no mutations in details. Assuming the mutation rates are sufficiently small, we obtain the results for the cases with forward mutation and forward-backward mutations by perturbation theory and a theorem of perturbation on global stability. There are three cases for the case of no mutations. Similar to the simple chemostat equation, the competitive exclusion principle holds. For Case 1, no drug injection , the wild type bacteria wins the competition. For Case 2, the drug injected continuously, the species with smallest break-even concentration in new simple chemostat equation , wins competition. For case 3, with dynamics of drug on-drug off infinitely many times, competitive exclusion principle still holds , however not in the form of steady state.

报告人简介：许世壁教授，1970年在National Tsing-Hua University获得理学学士学位，1976年在爱荷华大学获得博士学位，1987-1990任National Tsing-Hua University应用数学研究所所长；1998-2004任National Tsing-Hua University理学院院长。许世壁教授是生物数学领域的国际知名专家。在J. Math. Biol., SIAM J. Math. Anal., Math. Biosci., Bull. Math. Biol., J. Differ. Equations, J. Theoret. Biol.等国际知名期刊上发表论文100余篇，并出版专著2部。2011-2014年被授予讲座教授，2011年至今被授予National Tsing-Hua University杰出讲座教授。2013年当选SIAM Fellow。

报告时间：2023年9月21日15:30—16:00

报告地点：数学学院201报告厅