报告题目：A cross-infection model with diffusive environmental bacteria
报告人：赵晓强 教授 加拿大纽芬兰纪念大学
照片：
邀请人：白振国
报告时间：2021年11月6日（周六）19：30-21：30
腾讯会议ID：826 656 157
报告人简介：
赵晓强，加拿大纽芬兰纪念大学数学与统计系教授，该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位，1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究，在单调动力学、一致持久性、行波解和渐近传播速度、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止，他已在“Comm. Pure Appl. Math.、J. Eur. Math. Soc.、J. reine angew. Math.、J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.”等国际知名期刊上发表论文100余篇，并在Springer出版专著“Dynamical Systems in Population Biology”。赵教授个人主页：https://www.math.mun.ca/~zhao/
报告摘要：
In order to investigate the role that environmental bacteria played in the dynamics of hospital infections, we propose a cross-infection model with diffusive bacteria in the environment. Firstly, we prove the global existence, uniform boundedness and ultimate boundedness of solutions as well as the existence of a global attractor for the equivalent model. Secondly, we investigate a limiting system to establish the threshold dynamics for the model in terms of the basic reproduction numberR0by using the theories of monotone dynamical systems and chain transitive sets. More precisely, we show that ifR0≤1, then the infection-free steady state is globally stable; and ifR0>1, then the system has a globally stable endemic steady state. Finally, we use the numerical method to explore the influence of different diffusion coefficients onR0. In the case where the transmission rate is independent of diffusion coefficient, the numerical results indicate thatR0is decreasing with respect to the diffusion rate. In the case where the transmission rate is a function of diffusion coefficient, we find that in a less polluted environment,R0is a decreasing function with respect to the diffusion rate, which implies that the diffusion of bacteria is beneficial for patients; while in a more polluted environment,R0may increase with increasing diffusion rate, which means increasing diffusion of bacteria is harmful for the elimination of disease. Thistalkisbasedonjointwork with Danfeng Pang and Yanni Xiao.
