Simulate an Epidemic

In this section, you will explore modeling disease spread on a larger scale using a simulator based on mathematical equations.

Simulating Disease Spread at Different Scales

This Click & Learn has two simulators based on the SIR model:

  • The “Outbreak Simulator” (“SIR Model Basics” tab) can be used to model small-scale disease spread. It works by having you go through specific steps to simulate individuals moving between groups.
  • The “Epidemic Simulator” (“SIR Model Advanced” tab) can be used to model large-scale disease spread. It works by using mathematical equations to simulate how groups change at a population level.

The table summarizes the differences between the simulators.

Outbreak Simulator
(SIR Model Basics)		 Epidemic Simulator
(SIR Model Advanced)
What It Models Small-scale disease spread Large-scale disease spread
Initial Susceptible Individuals ( S ) 35 Up to 200,000
Initial Infectious Individuals ( I ) 1 Up to 3,000
Initial Removed Individuals ( R ) 0 Up to 200,000
Transmission Described by an individual-level probability Described by a population-level rate
Recovery Described by an individual-level probability Described by a population-level rate
Time Up to 25 days Up to 3 years
Vaccination Up to 1 individual/day Depends on “Initial Removed Individuals”
Basic Reproduction Number (R0) Not calculated Calculated
Effective Reproduction Number (Re) Not calculated Displayed as a graph
Herd Immunity Threshold (HIT) Not calculated Calculated

Explore Epidemic Dynamics Using the SIR Model

Use the “Epidemic Simulator” to explore the changes that occur in a large population as a disease spreads.

Settings

  • Enter your values in the input fields. These values will be used to simulate the number of individuals in each group for each day.
  • Select the “Simulate” button to generate results.

Results

  • The “SIR Graph” will appear once you select “Simulate.” Select the “Learn About Model Calculations” button to learn more about how this graph is generated.
  • Additional factors (R0, Re, and HIT), which can indicate whether an epidemic may occur, will also be calculated. Select their “Learn About” buttons for more information.
  • Select the “Re Graph” button to display a graph showing Re for each day.
  • Hover over either the “SIR Graph” or the “Re Graph” to display data for a specific day. (Because of how our model is set up, the numbers of individuals in each group may not be whole numbers. You can round them to the nearest whole number if needed.)

In this model, you can include vaccinated individuals as part of the “Initial Removed Individuals.” For example, if 200 individuals in a population of 1000 are vaccinated, enter the following:

  • Initial Susceptible Individuals: 799
  • Initial Infectious Individuals: 1
  • Initial Removed Individuals: 200

SIR Epidemic Simulator

Settings: (modifiable)

Transmission Rate (t)
  • Represents the average likelihood, per day, that a susceptible individual becomes infected.
  • A constant ranging from 1 to 150 (%) in this simulator. A larger t means transmission is more likely.
  • Values of t over 100% means that an infectious individual infects more than one susceptible individual per day. For example, if an infectious individual infects 1.3 susceptible individuals per day, t is 1.3 × 100 = 130%. You would enter a value of “130” in the simulator.
Recovery Rate (r)
  • Represents the average likelihood, per day, that an infectious individual recovers.
  • A constant ranging from 1 to 100 (%) in this simulator. A larger r means recovery is more likely.
  • Can be estimated based on how long an infection lasts. For example, if an infection lasts 5 days on average, r is about 1/5 = 0.2 = 20%. You would enter a value of “20” in the simulator.
Total Population (N)
1000

Results: (automatically displayed)

Full Data Table
Day Susceptible Infectious Removed
0 999 1 0
Re Data Table
Day Susceptible (number) Susceptible (proportion)
0 0 0 0
Learn About Model Calculations
R0
The average number of individuals a single infectious individual will infect throughout the course of their infection, if everyone else in the population is susceptible.
Learn About R0 and Re
Re
Effective Reproduction Number (Re): varies over time
The average number of individuals a single infectious individual will infect throughout the course of their infection, if some individuals in the population are immune.
HIT
The proportion of immune individuals needed in a population for that population to have herd immunity.
Learn About Immunity