The goal of the National Research Experience for Undergraduates Program (NREUP) at Lawrence Technological University is to introduce students from ethnic groups which are underrepresented in mathematics to the multifaceted techniques of mathematically modeling the spread of infectious diseases.

The primary focus of the project will be model building and rigorously showing how these models behave using dynamical systems theory. A secondary focus will be on simulating the systems numerically, performing parameter estimations, and validating with real-world data.

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Faculty Mentors

Participants

  • Antwan Green
  • Steven Harris
  • Jalen Jackson
  • Dayo Ogunmodede 
  • Noah Stamboulieh

Since emerging in early 2020, 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 lockdowns, travel restrictions, and a massive vaccine development and rollout initiative.

Throughout the pandemic, 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, such as those in Metro Detroit and broader Michigan, 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 dynamical systems models of disease spread, with a focus on 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.

  1. 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?
  2. Normal screening protocols like symptom reporting and temperature checks do not catch asymptomatic spreaders of COVID-19. Can we incorporate asymptomatic transmission into our models? Do these models justify the population-wide lockdowns and quarantines we have seen?
  3. 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, such as secondary waves of infection?

The program will focus on building mathematical models of infectious disease spread using tools from dynamical systems theory. This is an important application of mathematical epidemiology, which utilizes mathematical tools from several different topic areas, including calculus, linear algebra, differential equations, dynamical systems, and scientific computing.

  • Relevant topics: SIR model, Basic reproductive number, Extent of an outbreak
  • Background resource #1: Infectious Disease Modeling, Matthew D. Johnston (write-up) (video lecture)
  • Background resource #2: A dynamical framework for modeling fear of infection and frustration with social distancing in COVID-19 spread, Bruce Pell (video)
  • Relevant topics: Differentiation rules, Integration rules and techniques
  • Background resource: Calculus Online Textbook (MIT), Gilbert Strang (Chapters 1–8)
  • Relevant topics: Solving linear systems, matrix inverses, eigenvalues/vectors
  • Background resource: MATH 123 Lecture Notes, Matthew D. Johnston (June 20 – July 1 lectures)
  • Relevant topics: Nonlinear systems, phase portraits, linear stability analysis
  • Background resource #1: Prof. Johnston lecture notes: First-order DEs (qualitative approach), Non-Linear Systems of DEs
  • Background resource #2: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Stephen Strogatz
  • Relevant topics: Programming in R, Maple, and MATLAB
  • R:
    • Download (free!)
    • Solving DEs (Tutorial)
    • Text: Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities, Rebecca Sanft and Anne Walter
  • Maple: Solving DEs (Tutorial)
  • MATLAB: Solving DEs (Tutorial)
  • Matthew D. Johnston and Bruce Pell. 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. Wells, Lindsey Myers, Jeffrey Duncan, Jim Collins, Meagan C. Fitzpatrick, Alison P. Galvani, Abhishek Pandey, Racial disparities in COVID-19 mortality across Michigan, United States. EClinicalMedicine, 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. On-campus activities will take place in S126 and the remainder will be available through Zoom.

Student Events

Date Time Event
Monday, June 7 9-10:15 a.m. Introductions, Program Overview, and Campus Tour
Monday, June 7 1-2:15 p.m. Mini-Lecture: Mathematical Modeling
Tuesday, June 8 9-10:15 a.m. Mini-Lecture: Differential Equations
Tuesday, June 8 1-2:15 p.m. Mini-Lecture: Programming in R
Wednesday, June 9 9-10:15 a.m. Mini-Lecture: Linear Algebra / Linear Systems
Wednesday, June 9 1-2:00 p.m. Special Lecture: Abba Gumel (ASU) Mathematics of the Dynamics and Control of the COVID-19 Pandemic
Thursday, June 10 9-10:15 a.m. Mini-Lecture: Dynamical Systems
Friday, June 11 9-10:15 a.m. Mini-Lecture: Mathematical Writing (Overleaf)
Monday, June 14 9-10:15 a.m. Case Study #1: Disease Spread of Ebola
Tuesday, June 15 9-10:15 a.m. Case Study #2: Social Feedback on Disease Spread
Wednesday, June 16 9-10:15 a.m. Case Study #3: 2009 H1N1
Wednesday, June 16 1-4:00 p.m. Special Event: Society for Mathematical Biology Annual Meeting
Thursday, June 17 9-10:15 a.m. Case Study #4: Vaccination Modeling
Friday, June 18 9-10:15 a.m. Mini-Project Presentations
Monday, June 21 9-10:15 a.m. Research Methods: Literature Review
Wednesday, June 23 1-2:00 p.m. Special Lecture: Sibrina Collins (LTU)
Monday, June 28 9-10:15 a.m. Research Methods: Model Building
Wednesday, June 30 1-2:00 p.m. Special Lecture: Enahoro Iboi (Spelman College) Impact of Public Health Education Program on the Novel Coronavirus Outbreak in the United States
Monday, July 5 CAMPUS CLOSED Independence Day Observed
Tuesday, July 6 9-10:15 a.m. Research Methods: Model Analysis
Thursday, July 8 1-2:00 p.m. Special Lecture: Trachette Jackson (University of Michigan)
Monday, July 12 9-10:15 a.m. Research Methods: Model Validation
Wednesday, July 14 1-2:00 p.m. Special Lecture: Monica Jackson (America University)
Monday, July 19 9-10:15 a.m. Research Methods: Mathematical Communication
Wednesday, July 21 1-2:00 p.m. Career Panel: Frank Crosby (Naval Research), Gilles Gnacadja (AMGEN), Destiny Anyaiwe (LTU)
Friday, July 23 9-11:00 a.m. Final Project Presentations

Public Events

The events below are publicly available through the Zoom link. All talks below are from 1-2 p.m. ET unless indicated otherwise.

Date and time Speaker and Institution Title and Abstract
Wednesday, June 9 Abba Gumel (ASU) Mathematics of the Dynamics and Control of the COVID-19 Pandemic
Friday, June 18
9 - 10:15 a.m
NREUP Participants Mini-Project Presentations
Wednesday, June 23 Sibrina Collins (LTU) Superhero Science: The Next Time You Go to the Movies
Wednesday, June 30 Enahoro Iboi (Spelman College) Impact of Public Health Education Program on the Novel Coronavirus Outbreak in the United States
Thursday, July 8 Trachette Jackson (University of Michigan)
Wednesday, July 14 Monica Jackson (American University)
Wednesday, July 21 Frank Crosby (Naval Research)
Gilles Gnacadeja (AMGEN)
Destiny Anyaiwe (LTU)
Career Panel
Friday, July 23
9 - 11 a.m
NREUP Participants Final Project Presentations

Acknowledgements

Support for this program is provided through the Mathematical Association of America by the National Science Foundation,

Award #DMS-1950644.