# Mathematical modelling the coronavirus outbreak in the UK

Mar 4th, 2020
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1. Mathematical modelling the coronavirus outbreak in the UK
2. -----------------------------------------------------------
3.
4. This mathematical model includes the following:
5.
6. - 67 million population, reflecting the actual UK population.
7. - The population are modelled as individuals, like 'sims'.
8. - Variations in population density across the UK is taken into
9. consideration.
10. - Varying degrees of travel (local vs distant) is taken into consideration.
11. - Varying degrees of human-to-human contact is taken into consideration.
12. - Trends derived from worldwide coronavirus statistics, as accumulated
13. through february.
14. - Trends seen in similar infections, such as seasonal variations on spread of
15. infections.
16.
17. Disclaimer: Although of moderate complexity, this is only a model. Reality
18. may differ widely from, due to errors within the model, and because of
19. changes in human behaviour in response to the outbreak.
20.
21.
22. EARLY PREDICTIONS
23. -----------------
24.
25. There are always random elements in reality which cannot be guessed. I have
26. performed multiple simulations with random variations to see various possible
27. outcomes. The intervals given below are the interquartile range of these
28. multiple simulations.
29.
30.
31. Day Total Cases in the UK
32. ---------------------------------
33. S 01 Mar 20 - 32
34. M 02 Mar 31 - 46
35. T 03 Mar 42 - 66
36. W 04 Mar 61 - 83
37. T 05 Mar 82 - 109
38. F 06 Mar 113 - 147
39. S 07 Mar 165 - 202
40. S 08 Mar 226 - 259
41. M 09 Mar 335 - 418
42. T 10 Mar 437 - 572
43. W 11 Mar 564 - 802
44. T 12 Mar 727 - 1076
45. F 13 Mar 928 - 1398
46. S 14 Mar 1184 - 1868
47. S 15 Mar 1521 - 2555
48. M 16 Mar 1944 - 3377
49. T 17 Mar 2505 - 4508
50. W 18 Mar 3155 - 6012
51. T 19 Mar 4007 - 8094
52. F 20 Mar 4992 - 10747
53. S 21 Mar 6347 - 14390
54. S 22 Mar 7955 - 19299
55. M 23 Mar 9931 - 25882
56. T 24 Mar 12392 - 34742
57. W 25 Mar 15448 - 46387
58. T 26 Mar 19229 - 62262
59. F 27 Mar 23976 - 83502
60. S 28 Mar 29756 - 111521
61. S 29 Mar 36661 - 149147
62. M 30 Mar 45087 - 199013
63. T 31 Mar 55440 - 265889
64.
65.
66. LONGER TERM PREDICTIONS
67. -----------------------
68.
69. Continuing the simulations for longer, we see the spread of infection really
70. picks up pace through april, and reaches a peak somewhere between late
71. april and mid may.
72.
73. The peak number of 'sick' during this period of time is between 4.7% and
74. 11.0% of the population.
75.
76.
77. DATE Total Cases Total 'sick' at any one time
78. ---------------------------------------------------------
79. end MAR 55k - 266k 0.0% - 0.1% of total population
80.
81. mid APR 0.8M - 7.4M 0.5% - 5.0%
82. end APR 4.6M - 17.7M 3.2% - 11.0%
83.
84. mid MAY 9.8M - 23.6M 4.7% - 5.6%
85. end MAY 14.2M - 27.2M 3.1% - 3.7%
86.
87. mid JUN 17.4M - 29.3M 2.0% - 3.0%
88. end JUN 20.3M - 30.5M 1.1% - 2.6%
89.
90. JUN 25% - 44%
91. JUL 33% - 47%
92. AUG 41% - 48%
93. SEP 45% - 49%
94. OCT 46% - 50%
95. NOV 47% - 51%
96. DEC 47% - 51%
97.
98. During the summer months, the prevalence of the infection steadily declines.
99.
100. By mid july, between one third and one half of the population have
101. been infected.
102.
103. In the latter half of the year, the upper interquartile doesn't readily
104. alter, suggesting that no more than 51% of the population will become
105. infected.
106.
107. And by the end of the year, the lower interquartile catches up to the upper
108. interquartile, suggesting that at least 47% of the population will
109. become infected eventually.
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