Analysing the output

The results.csv.bz2 file contains all of the population trajectories from the nine model runs. You can explore this using Python pandas, R, or Excel as you did before. Using ipython or Jupyter notebooks with pandas, we can load up the file;

>>> import pandas as pd
>>> df = pd.read_csv("output/results.csv.bz2")
>>> print(df)
             fingerprint  repeat  beta[2]  too_ill_to_move[2]  day        date         S  E  I         R  IW   UV
     0        0i3v0i0       1      0.3                 0.0    0  2020-05-12  56082077  0  0         0   0  1.0
     1        0i3v0i0       1      0.3                 0.0    1  2020-05-13  56082077  0  0         0   0  1.0
     2        0i3v0i0       1      0.3                 0.0    2  2020-05-14  56082072  5  0         0   0  1.0
     3        0i3v0i0       1      0.3                 0.0    3  2020-05-15  56082072  0  5         0   0  1.0
     4        0i3v0i0       1      0.3                 0.0    4  2020-05-16  56082066  0  5         6   5  1.0
     ...          ...     ...      ...                 ...  ...         ...       ... .. ..       ...  ..  ...
     1769     0i5v0i5       1      0.5                 0.5  169  2020-10-28   6302422  1  0  49779654   0  1.0
     1770     0i5v0i5       1      0.5                 0.5  170  2020-10-29   6302422  0  1  49779654   0  1.0
     1771     0i5v0i5       1      0.5                 0.5  171  2020-10-30   6302422  0  1  49779654   0  1.0
     1772     0i5v0i5       1      0.5                 0.5  172  2020-10-31   6302422  0  1  49779654   0  1.0
     1773     0i5v0i5       1      0.5                 0.5  173  2020-11-01   6302422  0  0  49779655   0  1.0

     [1774 rows x 12 columns]

This is very similar to before, except now we have extra columns giving the values of the variables that are being adjusted (columns beta[2] and too_ill_to_move[2]. We also now have a use for the fingerprint column, which contains a unique identifier for each pair of adjustable variables.

Note

In the fingerprint the i character represents a decimal point and v separates variables. For example 0.3  0.0 becomes 0i3v0i0, while 0.5 0.5 becomes 0i5v0i5.

Finding peaks

We can use .groupby to group the results with the same fingerprint together. Then the .max function can be used to show the maximum values of selected columns from each group, e.g.

>>> df.groupby("fingerprint")[["day", "E","I", "IW", "R"]].max()
                              day        E         I    IW         R
      fingerprint
      0i3v0i0      223  1867602   9124999  8588  48107545
      0i3v0i25     213  1806030   8849753  8588  48080295
      0i3v0i5      203  1925482   9373635  8588  48050991
      0i4v0i0      191  1926941   9441320  8588  49044169
      0i4v0i25     209  2013614   9815751  8588  49007451
      0i4v0i5      196  2049927   9994566  8588  48979256
      0i5v0i0      177  2108287  10278260  8588  49861436
      0i5v0i25     180  2093600  10215078  8588  49814876
      0i5v0i5      173  2070325  10128212  8588  49779655

From this, we can see that higher peaks occured for higher values of beta, which is expected. However, different values of too_ill_to_move had little impact on the peaks.

Warning

Do not over-interpret the results of single runs, such as the above. There is a lot of random error in these calculations and multiple model runs must be averaged over to gain a good understanding.

Plotting the output

There are lots of plots you would likely want to draw, so it is recommended that you use a tool such as R, Pandas or Excel to create the plots that will let you explore the data in full. For a quick set of plots, you can again use metawards-plot to generate some overview plots. To do this type;

metawards-plot -i output/results.csv.bz2 --format jpg --dpi 150

Note

We have used the ‘jpg’ image format here are we want to create animations. You can choose from many different formats, e.g. ‘pdf’ for publication quality graphs, ‘png’ etc. Use the --dpi option to set the resolution when creating bitmap (png, jpg) images.

As there are multiple fingerprints, this will produce multiple overview graphs (one overview per fingerprint, and if you have run multiple repeats, then one average per fingerprint too).

The fingerprint value is included in the graph name, and they will all be plotted on the same axes. This means that they could be joined together into an animation. As well as plotting, metawards-plot has an animation mode that can be used to join images together. To run this, use;

metawards-plot --animate output/overview*.jpg

Note

You can only animate image files (e.g. jpeg, png). You can’t animate pdfs (yet - although pull requests welcome). Also, animation relies on you installing Pillow to create the gifs and (optional but recommended) gifsicle and pygifsicle to optimise the gifs (this reduces their size by 5-10 times)

Here is the animation.

Jupyter notebook

In addition, to the metawards-plot command, we also have a Jupyter notebook which you can look at which breaks down exactly how metawards-plot uses pandas and matplotlib to render multi-fingerprint graphs.