Lecture E3 (2022-10-20): Epidemic Dynamics

In this lecture, we start to introduce more complex system dynamics models (SDM), as would be implemented in Vensim or Insight Maker, for more complex systems. We focus on the classical SIR (susceptible–infectious–recovered) multi-compartment model from epidemiology. We build up this model as a stock-and-flow diagram from scratch, justifying the expressions/equations that we use and then using simulation to inform us when the equations might have significant flaws. Ultimately, we get to a working SIR model that matches dynamics of basic disease spread, and we go through a strategic thinking/scenario-planning example that shows that the value of quarantine policy is, in most cases, not to reduce spread of a disease but "flatten the curve" and lower (but widen) the infection peak to keep it under a manageable public-health threshold (set by university capacity/etc.).

Lecture E2 (2022-10-18): Making Simulations More Realistic, Part 2 – Delays, Fixed and Smoothing

In this lecture, we continue to add complexity to system dynamics models in Vensim and Insight Maker by introducing two different forms of delays – fixed delays and smoothing/averaging delays. We spend some of the lecture discussing the fundamental difference between these delays, and we spend much of the rest of the lecture discussing how to implement these delays in both Vensim and Insight Maker. We also discuss some other functions (like STEP, for step responses, and PULSE/PULSE TRAIN) as well as how to use lookup tables to insert more arbitrary functions over time as inputs to systems. Finally, we spend some time discussing how higher-order smoothing/averaging delays help mix aspects of both fixed delays and pure smoothing delays.

Lecture E1 (2022-10-14): Making Simulations More Realistic, Part 1 – Units, Sliders, and Lookup-Table Converters

In this lecture, we discuss how to embellish basic System Dynamics Modeling (SDM) simulation models with additional complexity and more efficiently interact with working simulation models. In particular, we introduce units (in both Vensim and Insight Maker) as a tool for the verification and validation of simulation models. We also discuss how to use sliders (in both Vensim and Insight Maker) to quickly adjust parameters (constants) and generate new outputs. We close with a discussion of lookup tables (converters) as well as how to implement them in both Vensim and Insight Maker. 

Lecture D-E (2022-09-29): Midterm Review

Midterm review session for ASU SOS 212 for Fall 2022.

Lecture D4 (2022-09-27): Chapter 3, Modelling Dynamic Systems (Morecroft, 2015)

In this lecture, we demonstrate how to draw and simulate stock-and-flow diagrams in Insight Maker (a web-based System Dynamics Modeling (SDM) tool), and then we discuss the third chapter of Morecroft (2015), which introduces the reader to stock-and-flow diagrams and numerical simulations of dynamical systems. We go through a simple example modeling the flows of instructors into and out of a university, and then we move to a more complex multi-sector simulation of a community attempting to regulate drug use through the use of police. This latter simulation helps illustrate how to form equations for flows and converter variables, and it also demonstrates how anomalous behaviors that are generated by simulations can help indicate where problems may be in simulation formulas (which should then be updated to make the simulation outputs more realistic).

Lecture D3 (2022-09-23): Stock-and-Flow Diagrams in Vensim and Insight Maker

In this lecture, we start by reviewing numerical integration methods (Euler's method) for approximating solutions to ordinary differential equations in spreadsheets. We use a filling toilet tank as an example of a balancing/negative-feedback system that we can simulate this way. We then pivot to discussing stock-and-flow diagram representations of these systems and then end with a short demonstration about how to use Vensim to draw and simulate these stock-and-flow diagrams, thereby greatly accelerating the numerical integration process done by hand in the spreadsheet. We ran out of time before being able to cover the example in Insight Maker, but we will start with that at the beginning of the next lecture.

Lecture D2 (2022-09-20): Introduction to Numerical Simulation of Dynamical Systems, Part 2

In this lecture, we review the fundamentals of numerical simulation (and Euler's method) for a simple clonal bacteria population system with only births. We then add a death flow in and explore how changing the numerical simulation time step ("dt") affects the results. We then transition to a numerical simulation of a toilet tank (a classic balancing feedback loop).