SIR-model-simulation

This is a very basic implementation of the SIR model for virus spreading. It lets you visualize how the three differential equations evolve over time, by printing a table to the terminal. This is the first part of my coding exam final project at University of Bologna, year one physics course.
All the code in this project (excluding external libraries) is written entirely by me (Matteo Bonacini).

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Dependencies

• Lyra (bundled)
• Doctest (bundled)
• CMake (recommended)
• gnuplot (optional)

Building

The preferred way to build this code is by using CMake.

mkdir build
cd build
cmake ..

Then, run either of these commands

make sir       # compile the program only
make sir-test  # compile tests only
make           # compile both

Both executables will be generated inside the build folder.

Running

This code was tested and running on Mac OS X 10.14.6 Mojave and Ubuntu 20.04 LTS (running on WSL).

Running via terminal

The easiest way to learn how to use this program is to read the help message.

$ ./sir --help
USAGE:
  <executable> [-?|-h|--help] -b|--beta <beta> -c|--gamma <gamma> -s|--susceptible <susceptible> [-i|--infected <infected>] [-r|--removed <removed>] -t|--day-count <dayCount> [--pretty] [--no-headings]

Display usage information.

OPTIONS, ARGUMENTS:
  -?, -h, --help
  -b, --beta <beta>       Beta constant. Must be a number in range [0, 1].
  -c, -g, --gamma <gamma>     Gamma constant. Must be a number in range [0, 1].
  -s, --susceptible <susceptible>
                          Number of susceptible people.
  -i, --infected <infected>
                          Number of infected people. Defaults to 1.
  -r, --removed <removed> Number of removed people. Defaults to 0.
  -t, --day-count <dayCount>
                          Duration of the simulation.
  --pretty                Prints a pretty table to the terminal.
  --no-headings           Remove headings from normal print.Ignored if --pretty is added as well.

Example run with pretty-print option enabled:

$ ./sir -b 0.2 -c 0.1 -s 1000 -t 160 --pretty
┌-----┬-----┬-----┬-----┐
│  T  │  S  │  I  │  R  │
├-----┼-----┼-----┼-----┤
│    1| 1000│    1│    0│
├-----┼-----┼-----┼-----┤
│    2| 1000│    1│    0│
├-----┼-----┼-----┼-----┤
│    3| 1000│    1│    0│
├-----┼-----┼-----┼-----┤
≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠
├-----┼-----┼-----┼-----┤
│  161|  198│    1│  802│
└-----┴-----┴-----┴-----┘

Example run with pretty-print option disabled:

$ ./sir -b 0.2 -c 0.1 -s 1000 -t 160 --no-headings
0 1000 1 0
1 1000 1 0
2 1000 1 0
3 1000 1 0
≠≠≠≠≠≠≠≠≠≠≠≠≠
160 198 1 802

Please note that the ≠ symbols mean that the output was truncated.
The four columns represent the number of susceptible (S), infected (I) and retired (R) people on each day (T) of the simulation. The initial state of the simulation is printed as well, which means that the number of rows printed is one more than the number specified using --day-count.

Graphing data

If you have gnuplot installed, you can use it to display the data.

./sir -b 0.2 -c 0.1 -s 1000 -t 160 | (    \
  cat > /tmp/sir-data &&                  \
  trap 'rm /tmp/sir-data' EXIT &&         \
  gnuplot -p -e                               \
  "plot for [col=2:4] '/tmp/sir-data'     \
  using 0:col with lines title columnheader")

The previous command will display the following graph:

If you are running on WSL 1, you might get this error:

gnuplot: error while loading shared libraries: libQt5Core.so.5: cannot open shared object file

It can be solved by running

sudo strip --remove-section=.note.ABI-tag /usr/lib/x86_64-linux-gnu/libQt5Core.so.5

Testing

Make sure to compile tests (see Building), then run

./sir-tests

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Components

What follows is a quick overview of the components that make up this program. Additional information is present in the comments alongside the code.

SIR Model

Class that handles the calculations of the SIR model. The model used consists of three differential equations:

Where S, I and R represent respectively the number of susceptible, infected and removed (dead/vaccinated/recovered) people. The equations are solved numerically, using an arbitrary value of dS = 1 day. The value of S is computed using the constraint that S + I + R is constant throughout the simulation. S, I and R are handled internally as double types, but the respective getter (or setter) functions will return (or accept) an integer value. This was done because these three variables represent natural numbers, but decimal numbers are required for solving the equations correctly.

Visualizer

Class that handles the display of table data. Its constructor takes a reference to a Model instance. The methods visualize and visualizePretty will run the model for the specified number of days. Please note that the Model instance will be altered by the visualizer.

Parser

Class that handles the parsing of command line arguments and exposes getter functions for them. The parsing is done using Lyra library (see dependencies). The parser checks that the input format is correct. The only value check performed here is for the --day-count parameter (if it is negative, an error is shown). This is not strictly needed, but it can be helpful to the user, since there are no explicit warnings for this anywhere else.
All the needed value checks on parameters are performed inside the Model class constructor.

Tests

Unit Tests are performed using Doctest and are built separately from the main executable. Tests are centered on the Model component, and they check that all the constraints imposed by the model are met. For additional information on how to run tests, see Testing.

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Additional notes

1. A requirement of the project was that there must be no memory leaks or illegal memory accesses. This program was run through Valgrind Memcheck and is completely devoid of them.
2. This code was run through Clang-Tidy to check for additional warnings. The configuration used was CLion default from JetBrains.