New Problems and New Methods in Biomathematics

Time: December 5th-7th, 2024

Venue: E10-320

Organizers:

Prof. Feng Yu, University of the Greater Bay Area

Prof. Lou Yuan, Shanghai Jiao Tong University

Prof. Zhou Zhennan, Westlake University

Schedule:

Titles and Abstracts (in order of the schedule):

Yanni Xiao, Xi'an Jiaotong University

Title: Co-evolution of behavior changes and disease transmission dynamics

Abstract: There are many challenges to quantifying and evaluating the impact of behavior changes on the disease spread and control. In this talk, we propose several mathematical models to fully investigate impact of behavioral changes on transmission dynamics of infectious diseases. Initially, I proposed the model with nonlinear incidence rate with/without delays to represent the effect of individuals’ psychological and behavioral changes. We apply this modelling approach to examine media impact on control of Covid-19 infection based on the multisource data. Then we proposed a multi-scale model which explicitly models both the disease transmission and information transmission to evaluate the effect of behavior changes on dynamic behaviors. Finally, I include the imitation dynamics to investigate how behavior changes, vaccination and relaxation of non-NPIs affect the development of COVID-19 infections. Finally I shall give some considerations and thoughts on modelling behavioral changes. This is a joint work with Jianhong Wu and Sanyi Tang.

Chen Jia, CSRC

Title：Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations

Abstract: Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on a sufficient long coarse-grained trajectory, we obtain a set of sufficient statistics which extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we completely solve the problems of parameter inference and nonequilibrium identification for a general Markovian system with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our nonequilibrium criterion generalizes the one obtained in [J. Chem. Phys. 132:041102 (2010)] for a three-state system with two coarse-grained clusters, and is much superior to the classical criterion based on autocorrelation functions.

Fangzhou Xiao, Westlake University

Title: Universal polyhedral constraints govern the behavior of biomolecular reaction systems

Abstract: The robust yet versatile behaviors of biological organisms act via biomolecular processes in cells that happen through catalysis by enzymes. To regulate the rate of these processes, substrates, regulator proteins, cofactors, and other helper molecules bind with the catalytic enzyme to change its activity. Existing methods to analyze regulation of catalytic processes require simplifications by over-abundance assumptions, exemplified by the Michaelis-Menten formula. However, recently uncovered complex regulatory circuits with combinatorial or highly dynamic behaviors in metabolic engineering and developmental and synthetic biology break these assumptions. This imminent future of science and engineering on biological systems calls for a method to capture the full regulatory profile for holistic analysis, without restrictive assumptions. In this talk I will show a novel foundation of bioregulation based on an analysis of binding networks using differential geometry and convex polyhedra that captures bioregulation holistically in terms of reaction order polyhedra (ROP). ROP can be tractably analyzed and scalably computed for arbitrary binding networks. It allows discovery of necessary and sufficient conditions for a circuit to achieve a certain function, thus revealing regimes hidden by traditional methods of analysis. It also promotes holistic comparisons of different circuit implementations, e.g. activating versus repressing, thus enabling biocircuit design where we know when a design will work, and when a design will fail. On dynamics and control of biocircuits, reaction order can work as a robust basis for stability, perfect adaptation, multistability, and oscillations. In summary, ROP serves as a holistic foundation of bioregulation upgrading the Michaelis-Menten formula used for over a century, paving the way for rational design and holistic analysis of dynamics in biocircuits.

Wei Lin, Fudan University

Title: How higher-order configurations influence intelligent complex systems?

Abstract: In traditional investigations of biological and ecological systems, as well as in artificial intelligence frameworks, linear or simple nonlinear configurations have typically been preferred for modeling and reconstructing real-world dynamics. However, recent advances suggest that higher-order configurations offer unexpected capabilities. These include stabilizing ecosystems, reconstructing complex systems, and modulating biological rhythms. This talk will illustrate these capabilities using several examples and offer perspectives on this promising research direction.

Min Tang, Shanghai Jiao Tong University

Title: Crossover from ballistic transportation to normal diffusion: a kinetic view

Abstract: Identifying various modes of dispersion is closely related to the resolution of experimental data and the measurement time scales. In many complex systems, a crossover behavior between different modes of dispersion is commonly observed.

In this talk, we shift our focus from solely phenomenological particle trajectories to an intracellular mechanism that facilitates a crossover from ballistic transport to normal diffusion at the population level. Our results provides an intracellular mechanism for the crossover from ballistic transportation to normal diffusion at the population level

Ning Jiang, Wuhan University

Title: On self-organization kinetic models and hydrodynamics

Abstract: In this talk, we review some self-organization models arising in biology and physics, in particular, Vicsek model 1999 and its mathematical re-visit by Degond and Motsch in 2007. Starting from particle system, it can be derived the kinetic models (SOK) and more macroscopic hydrodynamic models (SOH). Together and Tengfei Zhang and Yi-long Luo, we made some rigorous justifications from SOK to SOH, using a Generalized Collision Invariants (GCI)-based Hilbert expansion. Moreover, our proof is employed some geometry of S^2 and SO(3).

Shuang Liu, Beijing Institute of Technology

Title: On Principal Eigenvalues for Elliptic Operators with Shear Flow

Abstract：In this talk, we will discuss the recent progress on principal eigenvalues of second order elliptic operators with shear flow. Some monotonicity and asymptotic behaviors of principal eigenvalues, with respect to diffusion rate and flow amplitude, are established. These local asymptotic analysis can help us find some global information on  the principal eigenvalue, i.e. the classification of topological structures of the level sets as a function of multiple parameters. This enables us to better understand qualitative properties of the principal eigenvalues.  This is a joint work with Professor Yuan Lou.

Jinzhi Lei, Tiangong University

题目：细胞增殖过程的若干问题讨论

摘要：本报告将介绍与细胞增殖过程相关的问题及其数学研究方法：（1）细胞分裂的过程中伴随DNA 的复制和DNA 甲基化的重构。 基因组的DNA 甲基化变化对早期胚胎、癌症发生和衰老等过程都有重要意义。本报告介绍伴随细胞分裂过程的 DNA 甲基化重构过程的数学描述，并讨论相关问题。（2）细胞增殖过程的数学描述包括细胞内信号通路和细胞群体动力学两个尺度的过程，对这两个尺度的动力学过程的数学描述需要不同的数学工具。本报告讨论如何建立整合的计算模型对细胞增殖过程中的不同尺度行为进行统一描述。

Zhigui Liu, Yangzhou University

Title: The stopping time and the spatial-temporal risk index in an epidemic model

Abstract: In this talk, we first consider a SIVR(susceptible-infected-vaccinated-recovered) model which combines impulsive vaccination into the classical SIR model. The final size, the peak value and peak time are studied, then the critical times for a given infected number is discussed, and it can be used to define and estimate the stopping time. Finally, a diffusion SIS model is proposed to study the spatial spreading of virus. The free boundary is introduced to describe the spreading front of the infected interval. To check the effect of spatial heterogeneity and habitat characteristic on the spreading of the virus, the spatial-temporal risk index is given. Our results show that the virus will spread in the high-risk habitat; In a low-risk habitat, small initial infected habitat, small initial numbers of the virus and fast diffusion are beneficial for the virus to vanish. When the virus spreads in the whole habitat, the asymptotic spreading speed is given.

Zhaoyin Xiang, University of Electronic Science and Technology of China

Title: On the global solvability of a chemotaxis-fluid system with logistic source

Abstract: In this talk, we focus on a chemotaxis-fluid system with logistic source in a bounded domain $\Omega\subset\mathbb{R}^N$ subject to no-flux/Dirichlet/Dirichlet boundary conditions for cells/signal/fluid, respectively. We will show that when $N =2$, the system admits a global bounded classical solution for any regular initial data. When $N =3$ similar conclusion holds provided that the logistic damping is strong enough in some sense. We will also give some stabilization analysis under some additional assumptions. This is a joint work with Dr Yifei Sun and Dr Yu Tian.    

Tiejun Li, Peking University

Title: AI Assisted Computational Biology: Two Case Studies

Abstract: AI opens the door for computational biology, in which some tough problems embrace the chance to be resolved. We will present two case studies recently done by our group: the non-equilibrium landscape construction and spatiotemporal dynamics for single cells from the scRNA-seq data analysis. One central aim is to show the fruitful integration of data and dynamics. It is a joint work with Dr. Wei Zhang, Yue Zhao, Peijie Zhou and Qiangwei Peng.

Xiaoqiang Sun, Sun Yat-sen University

题目: 肿瘤-微环境互作的动态建模和网络重构

摘要: 微环境在肿瘤生长和耐药中发挥着重要的作用。如何发展可解释可计算的数学理论与方法揭示肿瘤-微环境互作的多尺度调控规律是一个前沿而重要的问题。在此报告中，将介绍近年来我们采用模型-数据驱动的计算系统生物学研究范式在肿瘤-微环境互作的数学建模与数据分析方面的工作，包括：（1）肿瘤微环境多尺度系统的动力学建模、分析与控制；（2）基于单细胞/空间转录组数据的细胞通讯网络重构方法及其应用。

Maolin Zhou, Nankai University

Titile: Some Results on Nonlinear Porous Medium Equations

Abstract: In this talk, we will discuss about the porous medium equation with reaction terms, especially on the convergence of solutions and the propagation of free boundaries.

Zhou Peng, Shanghai Normal University

Title: On a Lotka-Volterra competitive patch model

Abstract: A Lotka-Volterra patch model describing the competition between two aquatic species is investigated, where organisms are supposed to take both random and advective movements. The global dynamics is determined in different settings of parameters, where sufficient analysis on the principal eigenvalue is performed to determine the local dynamics of the boundary equilibria and a technical approach is developed to establish the nonexistence of any positive equilibrium for any number of patches. This work can be seen as a further development of a series of works on the corresponding space-continuous PDE model.