报告人：牛瑞吾
主持人：吴晓群
日期：2024.07.15
时间：10:00am
地点：深圳大学致真楼801
Abstract
We present an SIR model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions.
However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdos-Renyi) networks compared to small-scale (Barabasi-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest non-zero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.
Bio
牛瑞吾，2019年博士毕业于武汉大学数学与统计学院，曾在深圳大学担任专职副研究员一职，并于期间获得一项国家自然科学基金青年项目，目前在香港城市大学做博士后工作。主要研究方向是：复杂网络，疾病传播，非线性动力系统。
