Calculate time trajectory of solution to a Susceptible-Infectious-Removed (SIR) system by numerically solving the multi-group ordinary differential equations
simodeSIR.RdCalculate time trajectory of solution to a Susceptible-Infectious-Removed (SIR) system by numerically solving the multi-group ordinary differential equations
Arguments
- transmrates
matrix of group-to-group (column-to-row) transmission rates
- recoveryrate
inverse of mean infectious period
- popsize
the population size of each group
- initR
initial number of each group already infected and removed (included in final size)
- initI
initial number of each group infectious
- initV
initial number of each group vaccinated
- times
optional argument for times at which the solution is to be calculated; if NULL (the default) the solution will be computed up to the time at which the total number of infectious individuals is sufficiently close to zero (outbreak extinction)
Examples
simodeSIR(transmrates = matrix(0.2, 2 ,2), recoveryrate = 0.3,
popsize = c(100, 150), initR = c(0, 0), initI = c(0, 1), initV = c(10, 10))
#> time S1 S2 I1 I2 R1
#> 1 0.000000 90.00000 139.00000 0.000000e+00 1.000000e+00 0.0000000
#> 2 3.333667 89.55461 138.31212 2.863860e-01 8.101482e-01 0.1590066
#> 3 6.667333 89.00733 137.46688 4.570141e-01 8.411435e-01 0.5356531
#> 4 10.001000 88.34071 136.43732 5.961351e-01 9.704711e-01 1.0631523
#> 5 13.334667 87.53725 135.19643 7.346865e-01 1.152992e+00 1.7280586
#> 6 16.668334 86.58104 133.71960 8.829578e-01 1.370414e+00 2.5360039
#> 7 20.002000 85.45987 131.98803 1.042251e+00 1.612175e+00 3.4978770
#> 8 23.335667 84.16787 129.99260 1.208921e+00 1.868022e+00 4.6232098
#> 9 26.669334 82.70806 127.73800 1.375862e+00 2.125278e+00 5.9160774
#> 10 30.003000 81.09448 125.24592 1.533423e+00 2.368410e+00 7.3720953
#> 11 33.336667 79.35304 122.55635 1.670550e+00 2.580117e+00 8.9764152
#> 12 36.670334 77.52058 119.72623 1.776354e+00 2.743497e+00 10.7030688
#> 13 40.004000 75.64206 116.82497 1.841911e+00 2.844735e+00 12.5160248
#> 14 43.337667 73.76611 113.92766 1.861877e+00 2.875567e+00 14.3720110
#> 15 46.671334 71.93997 111.10729 1.835408e+00 2.834686e+00 16.2246197
#> 16 50.005001 70.20494 108.42763 1.766166e+00 2.727746e+00 18.0288909
#> 17 53.338667 68.59312 105.93826 1.661435e+00 2.565995e+00 19.7454474
#> 18 56.672334 67.12593 103.67227 1.530663e+00 2.364025e+00 21.3434070
#> 19 60.006001 65.81433 101.64657 1.383908e+00 2.137370e+00 22.8017632
#> 20 63.339667 64.66016 99.86403 1.230525e+00 1.900477e+00 24.1093112
#> 21 66.673334 63.65822 98.31659 1.078304e+00 1.665381e+00 25.2634711
#> 22 70.007001 62.79840 96.98865 9.330987e-01 1.441118e+00 26.2684974
#> 23 73.340667 62.06767 95.86007 7.988154e-01 1.233727e+00 27.1335160
#> 24 76.674334 61.45165 94.90866 6.776661e-01 1.046616e+00 27.8706815
#> 25 80.008001 60.93583 94.11200 5.705125e-01 8.811263e-01 28.4936598
#> 26 83.341668 60.50629 93.44861 4.772481e-01 7.370833e-01 29.0164588
#> 27 86.675334 60.15025 92.89871 3.971189e-01 6.133280e-01 29.4526344
#> 28 90.009001 59.85622 92.44461 3.289968e-01 5.081176e-01 29.8147810
#> 29 93.342668 59.61416 92.07076 2.715767e-01 4.194352e-01 30.1142622
#> 30 96.676334 59.41538 91.76375 2.235126e-01 3.452027e-01 30.3611066
#> 31 100.010001 59.25248 91.51217 1.835073e-01 2.834169e-01 30.5640085
#> 32 103.343668 59.11921 91.30634 1.503621e-01 2.322259e-01 30.7304260
#> 33 106.677334 59.01031 91.13815 1.230015e-01 1.899689e-01 30.8666839
#> 34 110.011001 58.92144 91.00089 1.004855e-01 1.551942e-01 30.9780728
#> 35 113.344668 58.84898 90.88898 8.200198e-02 1.266475e-01 31.0690207
#> 36 116.678335 58.78993 90.79779 6.685896e-02 1.032600e-01 31.1432074
#> 37 120.012001 58.74185 90.72353 5.447285e-02 8.413028e-02 31.2036736
#> 38 123.345668 58.70272 90.66309 4.435526e-02 6.850423e-02 31.2529233
#> 39 126.679335 58.67088 90.61392 3.609957e-02 5.575380e-02 31.2930160
#> 40 130.013001 58.64499 90.57393 2.936905e-02 4.535886e-02 31.3256400
#> 41 133.346668 58.62394 90.54141 2.388595e-02 3.689051e-02 31.3521765
#> 42 136.680335 58.60682 90.51498 1.942167e-02 2.999571e-02 31.3737551
#> 43 140.014001 58.59291 90.49350 1.578840e-02 2.438431e-02 31.3912991
#> 44 143.347668 58.58161 90.47604 1.283259e-02 1.981921e-02 31.4055602
#> 45 146.681335 58.57242 90.46185 1.042872e-02 1.610659e-02 31.4171506
#> 46 150.015002 58.56496 90.45032 8.474194e-03 1.308796e-02 31.4265692
#> 47 153.348668 58.55889 90.44096 6.885384e-03 1.063404e-02 31.4342223
#> 48 156.682335 58.55397 90.43335 5.593983e-03 8.639566e-03 31.4404405
#> 49 160.016002 58.54996 90.42717 4.544467e-03 7.018766e-03 31.4454924
#> 50 163.349668 58.54671 90.42214 3.691730e-03 5.701691e-03 31.4495963
#> 51 166.683335 58.54407 90.41807 2.998907e-03 4.631548e-03 31.4529301
#> 52 170.017002 58.54193 90.41475 2.435960e-03 3.762236e-03 31.4556382
#> 53 173.350668 58.54018 90.41206 1.978638e-03 3.056006e-03 31.4578379
#> 54 176.684335 58.53877 90.40988 1.607218e-03 2.482175e-03 31.4596246
#> 55 180.018002 58.53762 90.40810 1.305459e-03 2.016113e-03 31.4610759
#> 56 183.351669 58.53668 90.40666 1.060257e-03 1.637653e-03 31.4622548
#> 57 186.685335 58.53593 90.40549 8.612047e-04 1.330154e-03 31.4632121
#> 58 190.019002 58.53531 90.40454 6.996215e-04 1.080318e-03 31.4639894
#> 59 193.352669 58.53481 90.40376 5.682716e-04 8.775199e-04 31.4646209
#> 60 196.686335 58.53440 90.40314 4.614818e-04 7.128237e-04 31.4651341
#> 61 200.020002 58.53407 90.40263 3.748048e-04 5.789374e-04 31.4655508
#> 62 203.353669 58.53381 90.40221 3.043703e-04 4.701040e-04 31.4658896
#> 63 206.687335 58.53359 90.40188 2.472979e-04 3.819520e-04 31.4661640
#> 64 210.021002 58.53341 90.40160 2.008706e-04 3.102352e-04 31.4663872
#> 65 213.354669 58.53327 90.40138 1.631560e-04 2.519739e-04 31.4665685
#> 66 216.688336 58.53315 90.40120 1.325221e-04 2.046674e-04 31.4667158
#> 67 220.022002 58.53306 90.40105 1.076373e-04 1.662449e-04 31.4668354
#> 68 223.355669 58.53298 90.40094 8.742833e-05 1.350301e-04 31.4669326
#> 69 226.689336 58.53292 90.40084 7.101525e-05 1.096738e-04 31.4670115
#> 70 230.023002 58.53287 90.40076 5.768082e-05 8.908275e-05 31.4670756
#> 71 233.356669 58.53283 90.40070 4.684893e-05 7.235942e-05 31.4671277
#> 72 236.690336 58.53279 90.40065 3.805316e-05 5.877246e-05 31.4671700
#> 73 240.024002 58.53276 90.40060 3.087138e-05 4.767631e-05 31.4672045
#> 74 243.357669 58.53274 90.40057 2.510544e-05 3.877282e-05 31.4672322
#> 75 246.691336 58.53272 90.40054 2.037421e-05 3.146916e-05 31.4672550
#> 76 250.025003 58.53271 90.40052 1.653658e-05 2.554231e-05 31.4672734
#> 77 253.358669 58.53270 90.40050 1.342305e-05 2.073160e-05 31.4672884
#> 78 256.692336 58.53269 90.40049 1.089571e-05 1.682698e-05 31.4673006
#> 79 260.026003 58.53268 90.40047 8.843851e-06 1.365829e-05 31.4673104
#> 80 263.359669 58.53267 90.40046 7.178224e-06 1.108656e-05 31.4673184
#> 81 266.693336 58.53267 90.40046 5.826387e-06 8.998921e-06 31.4673249
#> 82 270.027003 58.53267 90.40045 4.729264e-06 7.304197e-06 31.4673302
#> 83 273.360669 58.53266 90.40044 3.838751e-06 5.928604e-06 31.4673345
#> 84 276.694336 58.53266 90.40044 3.115864e-06 4.812159e-06 31.4673380
#> 85 280.028003 58.53266 90.40044 2.529068e-06 3.906013e-06 31.4673408
#> 86 283.361670 58.53265 90.40043 2.052790e-06 3.170484e-06 31.4673431
#> 87 286.695336 58.53265 90.40043 1.666228e-06 2.573425e-06 31.4673449
#> 88 290.029003 58.53265 90.40043 1.352467e-06 2.088793e-06 31.4673464
#> 89 293.362670 58.53265 90.40043 1.097781e-06 1.695439e-06 31.4673477
#> 90 296.696336 58.53265 90.40043 8.910483e-07 1.376172e-06 31.4673487
#> 91 300.030003 58.53265 90.40043 7.232472e-07 1.117025e-06 31.4673495
#> 92 303.363670 58.53265 90.40043 5.870501e-07 9.066727e-07 31.4673501
#> 93 306.697336 58.53265 90.40042 4.765026e-07 7.359298e-07 31.4673506
#> 94 310.031003 58.53265 90.40042 3.867712e-07 5.973425e-07 31.4673511
#> 95 313.364670 58.53265 90.40042 3.139360e-07 4.848555e-07 31.4673514
#> 96 316.698337 58.53265 90.40042 2.548166e-07 3.935515e-07 31.4673517
#> 97 320.032003 58.53265 90.40042 2.068309e-07 3.194402e-07 31.4673519
#> 98 323.365670 58.53265 90.40042 1.678821e-07 2.592845e-07 31.4673521
#> 99 326.699337 58.53265 90.40042 1.362677e-07 2.104572e-07 31.4673523
#> 100 330.033003 58.53265 90.40042 1.106065e-07 1.708253e-07 31.4673524
#> 101 333.366670 58.53265 90.40042 8.977757e-08 1.386567e-07 31.4673525
#> 102 336.700337 58.53265 90.40042 7.287115e-08 1.125457e-07 31.4673526
#> 103 340.034003 58.53265 90.40042 5.914854e-08 9.135165e-08 31.4673527
#> 104 343.367670 58.53265 90.40042 4.801007e-08 7.414877e-08 31.4673527
#> 105 346.701337 58.53265 90.40042 3.896908e-08 6.018551e-08 31.4673527
#> 106 350.035004 58.53265 90.40042 3.162444e-08 4.884221e-08 31.4673528
#> 107 353.368670 58.53265 90.40042 2.562272e-08 3.957289e-08 31.4673528
#> 108 356.702337 58.53265 90.40042 2.033826e-08 3.141133e-08 31.4673528
#> 109 360.036004 58.53265 90.40042 1.683598e-08 2.600225e-08 31.4673529
#> 110 363.369670 58.53265 90.40042 1.393680e-08 2.152462e-08 31.4673529
#> 111 366.703337 58.53265 90.40042 1.153686e-08 1.781805e-08 31.4673529
#> 112 370.037004 58.53265 90.40042 9.550198e-09 1.474975e-08 31.4673529
#> 113 373.370670 58.53265 90.40042 7.905639e-09 1.220982e-08 31.4673529
#> 114 376.704337 58.53265 90.40042 6.544276e-09 1.010727e-08 31.4673529
#> 115 378.715709 58.53265 90.40042 5.856351e-09 9.044810e-09 31.4673529
#> R2
#> 1 0.0000000
#> 2 0.8777359
#> 3 1.6919758
#> 4 2.5922061
#> 5 3.6505815
#> 6 4.9099821
#> 7 6.3997995
#> 8 8.1393799
#> 9 10.1367177
#> 10 12.3856682
#> 11 14.8635289
#> 12 17.5302782
#> 13 20.3302986
#> 14 23.1967704
#> 15 26.0580229
#> 16 28.8446201
#> 17 31.4957464
#> 18 33.9637064
#> 19 36.2160563
#> 20 38.2354920
#> 21 40.0180271
#> 22 41.5702355
#> 23 42.9062072
#> 24 44.0447206
#> 25 45.0068733
#> 26 45.8143086
#> 27 46.4879576
#> 28 47.0472726
#> 29 47.5098049
#> 30 47.8910425
#> 31 48.2044130
#> 32 48.4614356
#> 33 48.6718785
#> 34 48.8439124
#> 35 48.9843765
#> 36 49.0989536
#> 37 49.1923403
#> 38 49.2684037
#> 39 49.3303246
#> 40 49.3807107
#> 41 49.4216949
#> 42 49.4550217
#> 43 49.4821175
#> 44 49.5041430
#> 45 49.5220436
#> 46 49.5365902
#> 47 49.5484101
#> 48 49.5580137
#> 49 49.5658159
#> 50 49.5721543
#> 51 49.5773032
#> 52 49.5814856
#> 53 49.5848829
#> 54 49.5876425
#> 55 49.5898840
#> 56 49.5917044
#> 57 49.5931830
#> 58 49.5943838
#> 59 49.5953591
#> 60 49.5961514
#> 61 49.5967951
#> 62 49.5973183
#> 63 49.5977421
#> 64 49.5980869
#> 65 49.5983670
#> 66 49.5985944
#> 67 49.5987792
#> 68 49.5989292
#> 69 49.5990511
#> 70 49.5991501
#> 71 49.5992306
#> 72 49.5992959
#> 73 49.5993492
#> 74 49.5993920
#> 75 49.5994271
#> 76 49.5994556
#> 77 49.5994788
#> 78 49.5994975
#> 79 49.5995128
#> 80 49.5995251
#> 81 49.5995352
#> 82 49.5995433
#> 83 49.5995499
#> 84 49.5995553
#> 85 49.5995596
#> 86 49.5995632
#> 87 49.5995661
#> 88 49.5995684
#> 89 49.5995703
#> 90 49.5995718
#> 91 49.5995731
#> 92 49.5995741
#> 93 49.5995749
#> 94 49.5995756
#> 95 49.5995761
#> 96 49.5995765
#> 97 49.5995769
#> 98 49.5995772
#> 99 49.5995774
#> 100 49.5995776
#> 101 49.5995778
#> 102 49.5995779
#> 103 49.5995780
#> 104 49.5995781
#> 105 49.5995781
#> 106 49.5995782
#> 107 49.5995782
#> 108 49.5995783
#> 109 49.5995783
#> 110 49.5995783
#> 111 49.5995783
#> 112 49.5995784
#> 113 49.5995784
#> 114 49.5995784
#> 115 49.5995784
simodeSIR(transmrates = matrix(0.2, 2 ,2), recoveryrate = 0.3,
popsize = c(100, 150), initR = c(0, 0), initI = c(0, 1), initV = c(10, 10), times = 0:10)
#> time S1 S2 I1 I2 R1 R2
#> 1 0 90.00000 139.0000 0.0000000 1.0000000 0.00000000 0.0000000
#> 2 1 89.87609 138.8086 0.1072210 0.9064177 0.01669000 0.2849559
#> 3 2 89.74407 138.6047 0.1936700 0.8479245 0.06226244 0.5473490
#> 4 3 89.60349 138.3876 0.2651112 0.8160189 0.13139526 0.7963634
#> 5 4 89.45391 138.1566 0.3258273 0.8044142 0.22025939 1.0389863
#> 6 5 89.29486 137.9110 0.3789958 0.8084720 0.32614081 1.2805723
#> 7 6 89.12587 137.6500 0.4269846 0.8247553 0.44714292 1.5252861
#> 8 7 88.94646 137.3729 0.4715463 0.8507354 0.58199021 1.7763932
#> 9 8 88.75616 137.0790 0.5139841 0.8845394 0.72985954 2.0365080
#> 10 9 88.55447 136.7675 0.5552629 0.9247796 0.89026573 2.3077591
#> 11 10 88.34093 136.4377 0.5960943 0.9704230 1.06297337 2.5919149