Sorceress

Mathematical modelling the coronavirus outbreak in the UK

Mar 4th, 2020
1,244
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
  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.
RAW Paste Data