The script I created yesterday was a useful demonstration of reproduction numbers, but wasn’t an entirely accurate depiction of what would happen. Specifically, it only showed the number infected during each generation of infection, which artificially improves the effect of halving the reproduction number.
I’ve therefore added a little bit to the script to more accurately reflect what would happen:
Kent and Medway Population = 1846455
Number infected = 79, days = 0
Number infected = 197.5, days = 5, Cumulative Number infected = 276.5
Number infected = 493.75, days = 10, Cumulative Number infected = 770.25
Number infected = 1234.375, days = 15, Cumulative Number infected = 2004.625
Number infected = 3085.9375, days = 20, Cumulative Number infected = 5090.5625
Number infected = 7714.84375, days = 25, Cumulative Number infected = 12805.40625
Number infected = 19287.109375, days = 30, Cumulative Number infected = 32092.515625
Number infected = 48217.7734375, days = 35, Cumulative Number infected = 80310.2890625
Number infected = 120544.43359375, days = 40, Cumulative Number infected = 200854.72265625
Number infected = 301361.08398438, days = 45, Cumulative Number infected = 502215.80664062
Number infected = 753402.70996094, days = 50, Cumulative Number infected = 1255618.5166016
Number infected = 1883506.7749023, days = 55, Cumulative Number infected = 3139125.2915039
If we halve the reproduction number
Kent and Medway Population = 1846455
Number infected = 79, days = 0
Number infected = 98.75, days = 5, Cumulative Number infected = 177.75
Number infected = 123.4375, days = 10, Cumulative Number infected = 301.1875
Number infected = 154.296875, days = 15, Cumulative Number infected = 455.484375
Number infected = 192.87109375, days = 20, Cumulative Number infected = 648.35546875
Number infected = 241.0888671875, days = 25, Cumulative Number infected = 889.4443359375
Number infected = 301.36108398438, days = 30, Cumulative Number infected = 1190.8054199219
Number infected = 376.70135498047, days = 35, Cumulative Number infected = 1567.5067749023
Number infected = 470.87669372559, days = 40, Cumulative Number infected = 2038.3834686279
Number infected = 588.59586715698, days = 45, Cumulative Number infected = 2626.9793357849
Number infected = 735.74483394623, days = 50, Cumulative Number infected = 3362.7241697311
Number infected = 919.68104243279, days = 55, Cumulative Number infected = 4282.4052121639
Number infected = 1149.601303041, days = 60, Cumulative Number infected = 5432.0065152049
Number infected = 1437.0016288012, days = 65, Cumulative Number infected = 6869.0081440061
Number infected = 1796.2520360015, days = 70, Cumulative Number infected = 8665.2601800077
Number infected = 2245.3150450019, days = 75, Cumulative Number infected = 10910.57522501
Number infected = 2806.6438062524, days = 80, Cumulative Number infected = 13717.219031262
Number infected = 3508.3047578155, days = 85, Cumulative Number infected = 17225.523789077
Number infected = 4385.3809472694, days = 90, Cumulative Number infected = 21610.904736347
Number infected = 5481.7261840867, days = 95, Cumulative Number infected = 27092.630920434
Number infected = 6852.1577301084, days = 100, Cumulative Number infected = 33944.788650542
Number infected = 8565.1971626355, days = 105, Cumulative Number infected = 42509.985813177
Number infected = 10706.496453294, days = 110, Cumulative Number infected = 53216.482266472
Number infected = 13383.120566618, days = 115, Cumulative Number infected = 66599.60283309
Number infected = 16728.900708272, days = 120, Cumulative Number infected = 83328.503541362
Number infected = 20911.125885341, days = 125, Cumulative Number infected = 104239.6294267
Number infected = 26138.907356676, days = 130, Cumulative Number infected = 130378.53678338
Number infected = 32673.634195845, days = 135, Cumulative Number infected = 163052.17097922
Number infected = 40842.042744806, days = 140, Cumulative Number infected = 203894.21372403
Number infected = 51052.553431007, days = 145, Cumulative Number infected = 254946.76715504
Number infected = 63815.691788759, days = 150, Cumulative Number infected = 318762.45894379
Number infected = 79769.614735949, days = 155, Cumulative Number infected = 398532.07367974
Number infected = 99712.018419936, days = 160, Cumulative Number infected = 498244.09209968
Number infected = 124640.02302492, days = 165, Cumulative Number infected = 622884.1151246
Number infected = 155800.02878115, days = 170, Cumulative Number infected = 778684.14390575
Number infected = 194750.03597644, days = 175, Cumulative Number infected = 973434.17988219
Number infected = 243437.54497055, days = 180, Cumulative Number infected = 1216871.7248527
Number infected = 304296.93121318, days = 185, Cumulative Number infected = 1521168.6560659
Number infected = 380371.16401648, days = 190, Cumulative Number infected = 1901539.8200824
UK Population = 66436000
Number infected = 1, days = 0
Number infected = 2.5, days = 5, Cumulative Number infected = 3.5
Number infected = 6.25, days = 10, Cumulative Number infected = 9.75
Number infected = 15.625, days = 15, Cumulative Number infected = 25.375
Number infected = 39.0625, days = 20, Cumulative Number infected = 64.4375
Number infected = 97.65625, days = 25, Cumulative Number infected = 162.09375
Number infected = 244.140625, days = 30, Cumulative Number infected = 406.234375
Number infected = 610.3515625, days = 35, Cumulative Number infected = 1016.5859375
Number infected = 1525.87890625, days = 40, Cumulative Number infected = 2542.46484375
Number infected = 3814.697265625, days = 45, Cumulative Number infected = 6357.162109375
Number infected = 9536.7431640625, days = 50, Cumulative Number infected = 15893.905273438
Number infected = 23841.857910156, days = 55, Cumulative Number infected = 39735.763183594
Number infected = 59604.644775391, days = 60, Cumulative Number infected = 99340.407958984
Number infected = 149011.61193848, days = 65, Cumulative Number infected = 248352.01989746
Number infected = 372529.02984619, days = 70, Cumulative Number infected = 620881.04974365
Number infected = 931322.57461548, days = 75, Cumulative Number infected = 1552203.6243591
Number infected = 2328306.4365387, days = 80, Cumulative Number infected = 3880510.0608978
Number infected = 5820766.0913467, days = 85, Cumulative Number infected = 9701276.1522446
Number infected = 14551915.228367, days = 90, Cumulative Number infected = 24253191.380611
Number infected = 36379788.070917, days = 95, Cumulative Number infected = 60632979.451529
Number infected = 90949470.177293, days = 100, Cumulative Number infected = 151582449.62882
If we halve the reproduction number
UK Population = 66436000
Number infected = 1, days = 0
Number infected = 1.25, days = 5, Cumulative Number infected = 2.25
Number infected = 1.5625, days = 10, Cumulative Number infected = 3.8125
Number infected = 1.953125, days = 15, Cumulative Number infected = 5.765625
Number infected = 2.44140625, days = 20, Cumulative Number infected = 8.20703125
Number infected = 3.0517578125, days = 25, Cumulative Number infected = 11.2587890625
Number infected = 3.814697265625, days = 30, Cumulative Number infected = 15.073486328125
Number infected = 4.7683715820312, days = 35, Cumulative Number infected = 19.841857910156
Number infected = 5.9604644775391, days = 40, Cumulative Number infected = 25.802322387695
Number infected = 7.4505805969238, days = 45, Cumulative Number infected = 33.252902984619
Number infected = 9.3132257461548, days = 50, Cumulative Number infected = 42.566128730774
Number infected = 11.641532182693, days = 55, Cumulative Number infected = 54.207660913467
Number infected = 14.551915228367, days = 60, Cumulative Number infected = 68.759576141834
Number infected = 18.189894035459, days = 65, Cumulative Number infected = 86.949470177293
Number infected = 22.737367544323, days = 70, Cumulative Number infected = 109.68683772162
Number infected = 28.421709430404, days = 75, Cumulative Number infected = 138.10854715202
Number infected = 35.527136788005, days = 80, Cumulative Number infected = 173.63568394003
Number infected = 44.408920985006, days = 85, Cumulative Number infected = 218.04460492503
Number infected = 55.511151231258, days = 90, Cumulative Number infected = 273.55575615629
Number infected = 69.388939039072, days = 95, Cumulative Number infected = 342.94469519536
Number infected = 86.73617379884, days = 100, Cumulative Number infected = 429.6808689942
Number infected = 108.42021724855, days = 105, Cumulative Number infected = 538.10108624275
Number infected = 135.52527156069, days = 110, Cumulative Number infected = 673.62635780344
Number infected = 169.40658945086, days = 115, Cumulative Number infected = 843.0329472543
Number infected = 211.75823681358, days = 120, Cumulative Number infected = 1054.7911840679
Number infected = 264.69779601697, days = 125, Cumulative Number infected = 1319.4889800848
Number infected = 330.87224502121, days = 130, Cumulative Number infected = 1650.3612251061
Number infected = 413.59030627651, days = 135, Cumulative Number infected = 2063.9515313826
Number infected = 516.98788284564, days = 140, Cumulative Number infected = 2580.9394142282
Number infected = 646.23485355705, days = 145, Cumulative Number infected = 3227.1742677853
Number infected = 807.79356694632, days = 150, Cumulative Number infected = 4034.9678347316
Number infected = 1009.7419586829, days = 155, Cumulative Number infected = 5044.7097934145
Number infected = 1262.1774483536, days = 160, Cumulative Number infected = 6306.8872417681
Number infected = 1577.721810442, days = 165, Cumulative Number infected = 7884.6090522101
Number infected = 1972.1522630525, days = 170, Cumulative Number infected = 9856.7613152626
Number infected = 2465.1903288157, days = 175, Cumulative Number infected = 12321.951644078
Number infected = 3081.4879110196, days = 180, Cumulative Number infected = 15403.439555098
Number infected = 3851.8598887745, days = 185, Cumulative Number infected = 19255.299443872
Number infected = 4814.8248609681, days = 190, Cumulative Number infected = 24070.12430484
Number infected = 6018.5310762101, days = 195, Cumulative Number infected = 30088.655381051
Number infected = 7523.1638452626, days = 200, Cumulative Number infected = 37611.819226313
Number infected = 9403.9548065783, days = 205, Cumulative Number infected = 47015.774032891
Number infected = 11754.943508223, days = 210, Cumulative Number infected = 58770.717541114
Number infected = 14693.679385279, days = 215, Cumulative Number infected = 73464.396926393
Number infected = 18367.099231598, days = 220, Cumulative Number infected = 91831.496157991
Number infected = 22958.874039498, days = 225, Cumulative Number infected = 114790.37019749
Number infected = 28698.592549372, days = 230, Cumulative Number infected = 143488.96274686
Number infected = 35873.240686715, days = 235, Cumulative Number infected = 179362.20343358
Number infected = 44841.550858394, days = 240, Cumulative Number infected = 224203.75429197
Number infected = 56051.938572993, days = 245, Cumulative Number infected = 280255.69286496
Number infected = 70064.923216241, days = 250, Cumulative Number infected = 350320.6160812
Number infected = 87581.154020301, days = 255, Cumulative Number infected = 437901.77010151
Number infected = 109476.44252538, days = 260, Cumulative Number infected = 547378.21262688
Number infected = 136845.55315672, days = 265, Cumulative Number infected = 684223.7657836
Number infected = 171056.9414459, days = 270, Cumulative Number infected = 855280.7072295
Number infected = 213821.17680738, days = 275, Cumulative Number infected = 1069101.8840369
Number infected = 267276.47100922, days = 280, Cumulative Number infected = 1336378.3550461
Number infected = 334095.58876152, days = 285, Cumulative Number infected = 1670473.9438076
Number infected = 417619.48595191, days = 290, Cumulative Number infected = 2088093.4297595
Number infected = 522024.35743988, days = 295, Cumulative Number infected = 2610117.7871994
Number infected = 652530.44679985, days = 300, Cumulative Number infected = 3262648.2339993
Number infected = 815663.05849982, days = 305, Cumulative Number infected = 4078311.2924991
Number infected = 1019578.8231248, days = 310, Cumulative Number infected = 5097890.1156238
Number infected = 1274473.528906, days = 315, Cumulative Number infected = 6372363.6445298
Number infected = 1593091.9111325, days = 320, Cumulative Number infected = 7965455.5556623
Number infected = 1991364.8889156, days = 325, Cumulative Number infected = 9956820.4445778
Number infected = 2489206.1111445, days = 330, Cumulative Number infected = 12446026.555722
Number infected = 3111507.6389306, days = 335, Cumulative Number infected = 15557534.194653
Number infected = 3889384.5486632, days = 340, Cumulative Number infected = 19446918.743316
Number infected = 4861730.685829, days = 345, Cumulative Number infected = 24308649.429145
Number infected = 6077163.3572863, days = 350, Cumulative Number infected = 30385812.786431
Number infected = 7596454.1966078, days = 355, Cumulative Number infected = 37982266.983039
Number infected = 9495567.7457598, days = 360, Cumulative Number infected = 47477834.728799
Number infected = 11869459.6822, days = 365, Cumulative Number infected = 59347294.410999
Number infected = 14836824.60275, days = 370, Cumulative Number infected = 74184119.013748
It’s worth noting that this is far from an accurate reflection of the complex modelling experts will have used when studying covid-19. I’m also fully aware that using a function would be a far more efficient way to create this code. I may do that if I get a spare couple of minutes later today.