The goal of the 国家本科生科研经验项目 (NREUP) at 利记sbo is to introduce students from ethnic groups which are underrepresented in mathematics to the multifaceted techniques of mathematically modeling the spread of infectious diseases.
Faculty Mentors
- Dr. Matthew D. Johnston ( mjohnsto1@ycdwkj666.com )
- Dr. Bruce Pell ( bpell@ycdwkj666.com )
Participants
- Antwan Green
- Steven Harris
- Jalen Jackson
- Dayo Ogunmodede
- Noah Stamboulieh
自2020年初出现以来, COVID-19 has affected over 100 million people worldwide and killed at least 3 million. The pandemic has prompted an unprecedented global response which has included global lock-downs, 旅行限制, 以及大规模的疫苗开发和推广计划.
在大流行期间, mathematical modeling has played a primary role in guiding public policy interventions by forecasting the disease’s spread under a variety of public policy interventions. The disease, meanwhile, has cruelly and disproportionately affected minority communities, 比如底特律大都会区和密歇根州更广大的地区, where the case mortality rate is over twice as high for blacks as whites.
The primary objective of this project is engaging black students in vital mathematical research with the goal of creating an enduring environment of opportunity and inclusion for the black community in the Metro Detroit region.
Research Focus
We will focus on developing and analyzing 动力系统 models of disease spread, 重点是COVID-19. We will start by considering the SIR (Susceptible-Infected-Removed) model for the spread of an infectious disease. We will then brainstorm for further features to incorporate in our models which would be relevant to the dynamical behavior of COVID-19. We have identified the following questions as starting points for our discussion.
- The spread and lethality of COVID-19 has varied significantly across different regions, age groups, and ethnicities. In light of this, can we meaningfully incorporate regional and demographic variation into our models? Do these models supporting implementing different interventions strategies for different subpopulations?
- Normal screening protocols like symptom reporting and temperature checks do not catch asymptomatic spreaders of COVID-19. 我们能否将无症状传播纳入我们的模型? Do these models justify the population-wide lock-downs and quarantines we have seen?
- The transmission of COVID-19 is influenced by social behavior while, conversely, adherence to restrictive social behaviors is influenced by the prevalence of disease. Can we capture the dynamic interplay between disease spread and social behavior in our models? Are these models sufficient to explain the disease dynamics we have seen, 比如感染的第二波?
The program will focus on building mathematical models of infectious disease spread using tools from 动力系统 theory. 这是数学流行病学的一个重要应用, which utilizes mathematical tools from several different topic areas, 包括微积分, linear algebra, 微分方程, 动力系统, 科学计算.
- Relevant topics: SIR模型基本繁殖数爆发范围
- 背景资源1: 传染病模型,马修·D. Johnston ( write-up ) ( video lecture )
- 背景资源2: A dynamical framework for modeling fear of infection and frustration with social distancing in COVID-19 spread, Bruce Pell ( video )
- Relevant topics: 微分规则,积分规则和技巧
- 背景资源: 微积分在线教材 (MIT) 吉尔伯特·斯特朗(第1-8章)
- Relevant topics: 求解线性系统,矩阵逆,特征值/向量
- 背景资源: 数学123课堂笔记 , Matthew D. 约翰斯顿(6月20日至7月1日讲座)
- Relevant topics: 一阶系统,线性系统,数值方法
- 背景资源1: 初等微分方程 威廉·特伦奇(第1、2、3章) & 10)
- 背景资源2: Prof. Johnston讲义: 一阶微分方程(解析和数值方法) , DEs的线性系统
- Relevant topics: 非线性系统,相位画像,线性稳定性分析
- 背景资源1: Prof. Johnston讲义: 一阶微分方程(定性方法) , 微分方程的非线性系统
- 背景资源2: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering Stephen Strogatz
- Matthew D. 约翰斯顿和布鲁斯·佩尔. A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread . Math. Biosci. Eng., 17(6):7892-7915, 2020.
- Alyssa S. Parpia, Isabel Martinez, Abdulrahman M. El-Sayed, Chad R. 威尔斯,林赛·迈尔斯,杰弗里·邓肯,吉姆·柯林斯,梅根·C. 菲茨帕特里克,艾莉森P. 伽伐尼,Abhishek Pandey, Racial disparities in COVID-19 mortality across Michigan, United States . 临床医学,33:100761,2021.
- Antwan Green, Project Title: Vivacious Vaccines and the Spread of Immunity
- Steven Harris, Project Title: College Residence Life COVID-19 Quarantine and Athletics Analysis
- Jalen Jackson, Project Title: The Impact of Social Distancing and Vaccination on Controlling COVID-19 Outbreaks in Michigan
- Temidayo Ogunmodede, Project Title: How COVID-19 Has Affected Individual States in the USA
- Noah Stamboulieh, Project Title: The Effect of the Vaccination Rate and Social Distancing on the Severity of Our COVID-19 Pandemic
The following is a schedule of group events, lectures, and presentations. Unscheduled time will be spent on independent and group research activities. 校内活动将在 S126 剩下的将通过Zoom提供.
Student Events
Date | Time | Event |
Monday, June 7 | 9-10:15 a.m. | 介绍,项目概述,校园参观 |
Monday, June 7 | 1-2:15 p.m. | Mini-Lecture: 数学建模 |
Tuesday, June 8 | 9-10:15 a.m. | Mini-Lecture: 微分方程 |
Tuesday, June 8 | 1-2:15 p.m. | Mini-Lecture: Programming in R |
6月9日星期三 | 9-10:15 a.m. | Mini-Lecture: 线性代数/线性系统 |
6月9日星期三 | 1-2:00 p.m. | Special Lecture: Abba Gumel (ASU) Mathematics of the Dynamics and Control of the COVID-19 Pandemic |
6月10日星期四 | 9-10:15 a.m. | Mini-Lecture: Dynamical Systems |
Friday, June 11 | 9-10:15 a.m. | Mini-Lecture: 数学写作(背面) |
Monday, June 14 | 9-10:15 a.m. | Case Study #1: 埃博拉病毒的传播 |
Tuesday, June 15 | 9-10:15 a.m. | Case Study #2: 疾病传播的社会反馈 |
6月16日星期三 | 9-10:15 a.m. | Case Study #3: 2009 H1N1 |
6月16日星期三 | 1-4:00 p.m. | Special Event: 数学生物学学会年会 |
6月17日星期四 | 9-10:15 a.m. | Case Study #4: 疫苗接种建模 |
Friday, June 18 | 9-10:15 a.m. | 小型的演讲 |
Monday, June 21 | 9-10:15 a.m. | Research Methods: 文献综述 |
6月23日星期三 | 1-2:00 p.m. | Special Lecture: 西布丽娜·柯林斯(利记sbo) |
Monday, June 28 | 9-10:15 a.m. | Research Methods: Model Building |
6月30日星期三 | 1-2:00 p.m. | Special Lecture: Enahoro Iboi(斯佩尔曼学院) Impact of Public Health Education Program on the Novel Corona virus Outbreak in the United States |
Monday, July 5 | CAMPUS CLOSED | 庆祝独立日 |
Tuesday, July 6 | 9-10:15 a.m. | Research Methods: Model Analysis |
Thursday, July 8 | 1-2:00 p.m. | Special Lecture: 哈切特·杰克逊(密歇根大学) |
Monday, July 12 | 9-10:15 a.m. | Research Methods: Model Validation |
7月14日星期三 | 1-2:00 p.m. | Special Lecture: 莫妮卡·杰克逊(美国大学) |
Monday, July 19 | 9-10:15 a.m. | Research Methods: 数学交流 |
7月21日星期三 | 1-2:00 p.m. | Career Panel: 弗兰克·克罗斯比(海军研究), Gilles Gnacadja (AMGEN), Destiny Anyaiwe (利记sbo) |
Friday, July 23 | 9-11:00 a.m. | 期末项目报告 |
Public Events
下面的事件是 公开的 通过缩放链接 . 下面所有的演讲都是从1-2点开始.m. ET,除非另有说明.
Date and time | 演讲者及机构 | 题目与摘要 |
6月9日星期三 | Abba Gumel (ASU) | Mathematics of the Dynamics and Control of the COVID-19 Pandemic |
Friday, June 18 9 - 10:15 a.m | NREUP参与者 | 小型的演讲 |
6月23日星期三 | 西布丽娜·柯林斯(利记sbo) | 超级英雄科学:下次你去看电影 |
6月30日星期三 | Enahoro Iboi(斯佩尔曼学院) | Impact of Public Health Education Program on the Novel Corona virus Outbreak in the United States |
Thursday, July 8 | 哈切特·杰克逊(密歇根大学) | |
7月14日星期三 | 莫妮卡·杰克逊(美国大学) | |
7月21日星期三 | 弗兰克·克罗斯比(海军研究) Gilles Gnacadeja (AMGEN) Destiny Anyaiwe (利记sbo) | Career Panel |
Friday, July 23 9 - 11 a.m | NREUP参与者 | 期末项目报告 |