# 2021年上海理工大学 “生物数学与动力系统”学术研讨会

 2021年11月26日，学校视频会议一教232腾讯会议：184 881 853 时 间 主持人 报告人 报告题目 8:30--9:10 原三领 崔景安(北京建筑大学) 异质性传染病动力学模型与应用 9:10--9:50 邹秀芬(武汉大学) Data-driven multi-scale mathematical modeling of SARS-CoV-2 infection 9:50--10:00 会间休息 10:00--10:40 邹秀芬 张伟年(四川大学) Bifurcations in Recurrent Neural Network Involving Transcendental Functions 10:40--11:20 李万同(兰州大学) Nonlocal Diffusion Equations with Free Boundaries 11:20--12:00 靳 祯（山西大学） Dynamic Modeling of COVID-19 午餐、午间休息 14:00--14:30 主持人 主题 宇振盛 开幕式、合影 14:30--15:10 崔景安 肖冬梅(上海交通大学) Propagation dynamics in a class of integro-differential equation 15:10--15:50 楼 元(上海交通大学) Patch models in advective environment 15:50-16:10 会间休息 16:10--16:50 楼 元 李文侠（华东师范大学） How likely can a point be in different Cantor sets 16:50--17:30 林  伟(复旦大学) Time series analytics: Causation detections and dynamics predictions

1：专家简介

2：报告摘要

Yuan Lou (楼 元)

Shanghai Jiao Tong University, Ohio State University

(上海交通大学, 美国俄亥俄州立大学)

Abstract: We study the dynamics of two competing species in three-patch models and investigate how network topology may affect the evolution of dispersal in advective environments. We posit that individuals can move between connected patches freely and they are also subject to the passive, directed drift. Either carrying capacity is assumed to be the same in all patches or the drift rates could vary. We found that there are notable differences for these models, which correspond to distinctive network topology. This talk is based on two joint works with Hongyan Jiang and King-Yeung Lam (BMB 2020, 2021).

Propagation dynamics in a class of integro-differential equation

Dongmei Xiao (肖冬梅)

Shanghai Jiao Tong University (上海交通大学)

Abstract: In this talk we will focus on integro-differential Fisher-KPP equations, and discuss the monotonicity, uniqueness and stability of traveling waves of the equations. This is based on joint works with Zhaoquan Xu.

Data-driven multi-scale mathematical modeling of SARS-CoV-2 infection

Xiufen Zou (邹秀芬)

Wuhan University (武汉大学)

Abstract: Based on available data for COVID-19, we presented two mathematical models for SARS-CoV-2 infection. One is the coinfection of SARS-CoV-2 and bacteria to investigate the dynamics of COVID-19 progress. Another is a multi-scale computational model to understand the heterogeneous progression of COVID-19 patients. Combining theoretical analysis, numerical simulations and quantitative computations, we revealed that initial bacterial infection and immune-related parameters have great influences on the severity degree and mortality in COVID-19 patients. We further identified that T cell exhaustion plays a key role in the transition between mild-moderate and severe symptoms. In addition, we quantified the efficacy of treating COVID-19 patients and investigated the effects of various therapeutic strategies. These results highlight the critical roles of IFN and T cell responses in regulating the stage transition during COVID-19 progression.

Time series analytics: Causation detections and dynamics predictions

Wei Lin (林 伟)

Fudan University (复旦大学)

Abstract:In this plenary talk, I will introduce some of our recent works on time series analytics, including directional interactions detections and dynamics predictions. Based on the theory of nonlinear dynamical systems as well as machine learning techniques, we develop several data-driven and model-free frameworks for realizing detections and predictions. Through comparing our frameworks with other existing methods in the literature, we show the advantages of our frameworks when they are used to deal with the data produced numerically by dynamical oscillators and collected by real experiments as well.

Nonlocal Diffusion Equations with Free Boundaries

Wantong Li (李万同)

Lanzhou University (兰州大学)

Abstract: We introduce and study a class of free boundary models with nonlocal diffusion. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model. Finally, as applications, we consider the dynamics of a nonlocal L-V competition model and a nonlocal epidemic model with free boundaries. This talk is based on joint works with Jia-Feng Cao (LUT), Yihong Du (UNE), Fang Li (SYU), Wenjie Ni (UNE) and Meng Zhao (NWNU).

How likely can a point be in different Cantor sets

Wenxia Li (李文侠)

Bifurcations in Recurrent Neural Network Involving Transcendental Functions

Weinian Zhang (张伟年)

Sichuan University (四川大学)

Abstract: In this talk we investigate bifurcations of a three-node recurrent neural network, in which the transcendental function tanh(x) and its iterates are involved. Those functions make computation so complicated that one hardly determine the number and distribution of all equilibria. We give a method to ignore the classic routine of discussion but display their saddle-node, pitchfork, and Hopf bifurcations.

Jing’an Cui (崔景安)

Beijing University of Civil Engineering and Architecture(北京建筑大学)

Dynamic Modeling of COVID-19

Zhen Jin (靳 祯)

Shanxi University (山西大学)

Abstract: The outbreak of the Corona Virus Disease 2019 (COVID-19) epidemic began since last December that has spread the fastest, caused the most extensive infections and has a huge impact on the safety of human life. Dynamical modelling is one of the useful methods to reveal the transmission rule of COVID-19 spread which is based on the internal transmission mechanism and can dynamically predict the future trend according to the current information. In the talk, we will introduce some of the transmission dynamics models of COVID-19 under intervention: homogeneous mixed dynamics model, network dynamics model, and household dynamics modelWe also evaluated isolation and other interventions measures.

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