MATH 496: Going Viral: Population Dynamics of Infectious Disease
As we all cope with a global pandemic, modeling the population dynamics of diseases like COVID-19 has become a matter of national importance. This course is an introduction to the construction, analysis, and interpretation of differential equation models for the population dynamics of infectious disease, including standard generic models and a model designed specifically for COVID-19. Mathematical methods will include stability analysis and numerical analysis. General background in differential equations (such as MATH 221) is required, but no background in stability analysis or numerical analysis will be assumed. There will be some computer programming in Matlab or R, but no specific programming background is required. This course will be taught as MATH 496/896 during the Second 5-Week Session of the Summer 2020 semester (July 13 to August 13).
Differential equation models for the population dynamics of infectious diseases fall into two broad categories: epidemic models, which track the short term progress of a disease outbreak, and endemic models, which look at what happens on a time scale long enough to require consideration of population change through birth and natural death.
Analysis of epidemic models uses some differential equation methods, but relies primarily on numerical methods. The numerical methods we need are sometimes taught in a differential equations course, but I will assume that nobody has seen this material. You will need to do some computer programming in Matlab or R. I will assume nobody has done this before either.
We will use epidemic models for two case studies. One of these will be a test of a claim made by Jared Diamond in "Guns, Germs, and Steel" that epidemic disease played a large role in the history of the Americas after 1492. The other will be the current COVID-19 crisis, which we will study using a model I created in March 2020.
Analysis of endemic models uses stability analysis. This is another topic that is sometimes taught in a DE course, but is not in our current MATH 221 course. I will again assume that nobody has seen this material. In addition to working out results for simple models with hand computation, we will use a numerical linear algebra program to predict what would eventually have happened if COVID-19 had arisen in the era before the development of vaccines.
The course format will include video lectures, Zoom meetings to address questions, regular homework assignments, two mid-term exams, and one or more projects. There will not be a final exam.
If you have any questions, contact Professor Ledder at gledder@unl.edu. If you want to learn more about Covid-19 population dynamics, there is an educational module on this that does not require the user to know anything about disease modeling, or even about differential equations. You can find it at http://www.math.unl.edu/covid-module.