Day 16 Pre-class Assignment: Introduction to Compartmental Modeling

Day 16 Pre-class Assignment: Introduction to Compartmental Modeling#

Student Name: Put your name here.

Goals for Today’s Pre-Class Assignment#

In this assignment, you will learn that:

  • Studying how a system changes is important in almost every field.

  • Compartmental models are useful tools for representing discipline-relevant models of changing systems.

  • Models are only useful if they are interpretable and all aspects of the model connect to the real-life scenario.

Assignment Instructions#

This assignment will introduce why studying change in systems is important in the sciences and social sciences, and how we can use compartmental models to analyze change in a system.

This assignment is due by 11:59 p.m. the night before class, and should be uploaded into the appropriate “Pre-class assignments” submission folder. Submission instructions can be found at the end of the notebook.

Part 1: Why should we study change? How should we study change?#

Part 1a: What is a system?#

A system can be defined as “an organized group of related objects or components that represents a real world phenomenon” [1]. Systems have defined boundaries, and they can interact with other systems or be components of larger systems [2].

Systems can be found in every field in the sciences and social sciences. Some examples of systems include (but aren’t limited to) [3]:

  • Natural systems (E.g., organ systems, ecosystems, solar systems)

  • Physical systems in engineering and physics (E.g., mechanical systems, electrical systems)

  • Social systems (E.g., economic systems, political systems, education systems)

Watch the Educational Video on Systems Thinking and Definition on YouTube to learn more about systems.

Question: What is an example of a system from your daily life or field of study? What components are in this system?

[Response area]: Write your answer here!

Part 1b: Why should we study how systems change?#

Most of the time, systems aren’t static - the components of a system and the system as a whole change.

For example, a system might involve:

  • change in time (E.g., temperature or heart rate)

  • change in space (E.g., temperature or elevation)

  • change in strategies (E.g., deciding whether to invest)

  • change in numbers (of people, molecules, stars, etc.)

  • change in prices
    and so on…

Question: What is a value or system that you deal with on a daily basis that is changing? What causes it to change?

[Response area]: Write your answer here!

Part 1c: What is a model?#

A model can be defined as an informative representation of a system or phenomenon [4]. Scientists, social scientists, mathematicians, and engineers use models to make it easier to study complex systems and how they change. Since models are merely representative of systems, they come with limitations and assumptions [5]. Models can be descriptive (describing what has previously happened in a system) or predictive (forecasting future outcomes) [6].

Models can take many different forms. Some examples of models include (but aren’t limited to) [6]:

  • Mathematical equations and formulas

  • Computer simulations

  • Physical scale models

  • Drawings and diagrams

  • Maps

  • 3-Dimensional structures

Question: What models have you seen in your daily life or field of study? What systems do these models represent?

[Response area]: Write your answer here!

Part 2: What is a compartmental model?#

A compartmental model is “a mathematical framework used to simulate how populations move between different states or compartments.” [3] While compartmental models can be used to study many different systems, they have been traditionally used to model infectious disease transmission.

Part 2a)#

Watch this video for an introduction to Compartmental models: Compartmental Models and Ordinary Differential Equations.

Note: The video refers to Ordinary Differential Equations and how we can use them to translate a conceptual compartmental model into math and then to code. The In Class will continue to only focus on the more conceptual side, but we will move towards coding compartmental models more concretely over the next several class periods!

In the Video above, we use the Plant Model as an example for a compartmental model. This provides us with an opportunity to talk about how the boxes and arrows in compartmental models can be used to represent things in the model. For example, the equations provided here are somewhat simplified (but still work reasonably well!) because we assume that water translates directly to plant growth and the transition happens immediately. As you get more comfortable with compartmental models, consider where the arrows represent indirect vs. direct affects on what is in the compartment!

Part 2b)#

Question: Thinking back to the earlier questions in the pre-class as well as the video above, write down at least 2 questions that you have about systems, models, or compartmental models. You will bring these questions to class to share and discuss!

[Response area]: Write your questions here: 1.
2.

In class, you will take what you learned from this pre-class assignment and create a compartmental model for a scenario with your group.

Sources#

Assignment Wrap-up#

Please fill out the form that appears when you run the code below. You must completely fill this out in order to receive credit for the assignment!

Please complete the CMSE 201 Pre-Class Survey to submit your feedback.

Congratulations, you’re done!#

Submit this assignment by uploading it to the course Desire2Learn web page. Go to the “Pre-Class Assignments” folder, find the appropriate submission link, and upload it there.

Copyright © 2026, Department of Computational Mathematics, Science and Engineering at Michigan State University, All rights reserved.

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