Mathematical modelling the coronavirus outbreak in the UK

Mathematical modelling the coronavirus outbreak in the UK
-----------------------------------------------------------

This mathematical model includes the following:

- 67 million population, reflecting the actual UK population.
- The population are modelled as individuals, like 'sims'.
- Variations in population density across the UK is taken into
consideration.
- Varying degrees of travel (local vs distant) is taken into consideration.
- Varying degrees of human-to-human contact is taken into consideration.
- Trends derived from worldwide coronavirus statistics, as accumulated
through february.
- Trends seen in similar infections, such as seasonal variations on spread of
infections.

Disclaimer: Although of moderate complexity, this is only a model. Reality
may differ widely from, due to errors within the model, and because of
changes in human behaviour in response to the outbreak.


EARLY PREDICTIONS
-----------------

There are always random elements in reality which cannot be guessed. I have
performed multiple simulations with random variations to see various possible
outcomes. The intervals given below are the interquartile range of these
multiple simulations.


Day         Total Cases in the UK
---------------------------------
S 01 Mar    20    - 32
M 02 Mar    31    - 46
T 03 Mar    42    - 66
W 04 Mar    61    - 83
T 05 Mar    82    - 109
F 06 Mar    113   - 147
S 07 Mar    165   - 202
S 08 Mar    226   - 259
M 09 Mar    335   - 418
T 10 Mar    437   - 572
W 11 Mar    564   - 802
T 12 Mar    727   - 1076
F 13 Mar    928   - 1398
S 14 Mar    1184  - 1868
S 15 Mar    1521  - 2555
M 16 Mar    1944  - 3377
T 17 Mar    2505  - 4508
W 18 Mar    3155  - 6012
T 19 Mar    4007  - 8094
F 20 Mar    4992  - 10747
S 21 Mar    6347  - 14390
S 22 Mar    7955  - 19299
M 23 Mar    9931  - 25882
T 24 Mar    12392 - 34742
W 25 Mar    15448 - 46387
T 26 Mar    19229 - 62262
F 27 Mar    23976 - 83502
S 28 Mar    29756 - 111521
S 29 Mar    36661 - 149147
M 30 Mar    45087 - 199013
T 31 Mar    55440 - 265889


LONGER TERM PREDICTIONS
-----------------------

Continuing the simulations for longer, we see the spread of infection really
picks up pace through april, and reaches a peak somewhere between late
april and mid may.

The peak number of 'sick' during this period of time is between 4.7% and
11.0% of the population.


DATE      Total Cases	     Total 'sick' at any one time
---------------------------------------------------------
end MAR   55k    - 266k      0.0% - 0.1% of total population

mid APR   0.8M   -  7.4M     0.5% - 5.0%
end APR   4.6M   - 17.7M     3.2% - 11.0%

mid MAY   9.8M   - 23.6M     4.7% - 5.6%
end MAY  14.2M   - 27.2M     3.1% - 3.7%

mid JUN  17.4M   - 29.3M     2.0% - 3.0%
end JUN  20.3M   - 30.5M     1.1% - 2.6%

JUN        25%   -   44%
JUL        33%   -   47%
AUG        41%   -   48%
SEP        45%   -   49%
OCT        46%   -   50%
NOV        47%   -   51%
DEC        47%   -   51%

During the summer months, the prevalence of the infection steadily declines.

By mid july, between one third and one half of the population have
been infected.

In the latter half of the year, the upper interquartile doesn't readily
alter, suggesting that no more than 51% of the population will become
infected.

And by the end of the year, the lower interquartile catches up to the upper
interquartile, suggesting that at least 47% of the population will
become infected eventually.