It is a surreal time to be a teaching a course on mathematical modeling. In the past, it has been important to sell students on why this is an important topic especially since it is such a difficult subject. However, but when students encounter headlines like "With COVID-19, modeling takes on life and death importance" (Science, March 27, 2020), the topic sells itself. There are lots of interesting (and pressing!) questions that models can help us answer and they provide a useful testbed for our ideas about how to mitigate the spread of disease without having to take a wait and see approach. Some models are called minimal models (or sometimes “toy models”) and are designed to help us get an intuitive understanding how a system works without trying to describe every complex aspect of human behavior. Despite all the factors that they ignore and the “unrealistic” assumptions (used to simplify the model to make it easier to understand), these models often provide surprisingly realistic predictions about the qualitative behavior of a system. Other models, such as those used to build epidemic forecasts, take the fundamental principles of those minimal models and incorporate realistic models of human behavior (transportation patterns, heterogeneous behavior, age dependent susceptibility and interaction patterns, and even behavioral adjustments in response to local information) to attempt to make predictions about what could happen under a variety of different scenarios. Qualitatively, these models tend to produce very similar results to minimal models, but they can be used to get significantly more accurate quantitative predictions as well as estimates about the uncertainty of those predictions. Over the last couple of weeks, I have tried to share bits and pieces of information (links and videos) about mathematical models to help my non-mathematician friends understand what types of things go into the forecasts and models that we hear about through the media. I have created some of these materials myself, but sometimes someone else says it far better than I ever could. This video by one of my favorite (mathematical) youtube channels 3Blue1Brown, explains epidemic models through visual demonstrations in way that is remarkably clear and informative. I had been thinking about doing something like this myself, but he does it far better than I could ever hope to. If you want to understand the minimal models for epidemics as well as how strategies like quarantining, transportation bans, social distancing, hand washing affect the spread of disease, then I highly recommend you check out this excellent video:
- Mark J. Panaggio