Two-compartment model with no recovery.
Arguments
- init
Named numeric vector, e.g.
c(S = 990, I = 10).- params
Named numeric vector, e.g.
c(beta = 0.002).- beta
Transmission rate (contacts per individual per time).
- N
Total population size. Optional — defaults to
sum(init).- b
Birth rate (per capita per time). Optional.
- d
Death rate (per capita per time). Optional.
- times
Numeric vector of output times.
- ...
Additional arguments passed to
ode_solver.
Details
Closed population (default): $$\frac{dS}{dt} = -\beta \frac{S I}{N}$$ $$\frac{dI}{dt} = \beta \frac{S I}{N}$$
Open population (when b / d are provided):
$$\frac{dS}{dt} = b N - \beta \frac{S I}{N} - d S$$
$$\frac{dI}{dt} = \beta \frac{S I}{N} - d I$$
In the closed case population size \(N = S + I\) is conserved.
Examples
# Closed population
model_si(
init = c(S = 990, I = 10),
params = c(beta = 0.002),
times = seq(0, 30, by = 0.1)
)
#> time S I
#> 1 0.0 990.0000 10.00000
#> 2 0.1 989.9980 10.00198
#> 3 0.2 989.9960 10.00396
#> 4 0.3 989.9941 10.00594
#> 5 0.4 989.9921 10.00792
#> 6 0.5 989.9901 10.00990
#> 7 0.6 989.9881 10.01189
#> 8 0.7 989.9861 10.01387
#> 9 0.8 989.9841 10.01585
#> 10 0.9 989.9822 10.01784
#> 11 1.0 989.9802 10.01982
#> 12 1.1 989.9782 10.02180
#> 13 1.2 989.9762 10.02379
#> 14 1.3 989.9742 10.02577
#> 15 1.4 989.9722 10.02776
#> 16 1.5 989.9703 10.02974
#> 17 1.6 989.9683 10.03173
#> 18 1.7 989.9663 10.03372
#> 19 1.8 989.9643 10.03570
#> 20 1.9 989.9623 10.03769
#> 21 2.0 989.9603 10.03968
#> 22 2.1 989.9583 10.04167
#> 23 2.2 989.9563 10.04365
#> 24 2.3 989.9544 10.04564
#> 25 2.4 989.9524 10.04763
#> 26 2.5 989.9504 10.04962
#> 27 2.6 989.9484 10.05161
#> 28 2.7 989.9464 10.05360
#> 29 2.8 989.9444 10.05559
#> 30 2.9 989.9424 10.05758
#> 31 3.0 989.9404 10.05957
#> 32 3.1 989.9384 10.06157
#> 33 3.2 989.9364 10.06356
#> 34 3.3 989.9344 10.06555
#> 35 3.4 989.9325 10.06754
#> 36 3.5 989.9305 10.06954
#> 37 3.6 989.9285 10.07153
#> 38 3.7 989.9265 10.07353
#> 39 3.8 989.9245 10.07552
#> 40 3.9 989.9225 10.07752
#> 41 4.0 989.9205 10.07951
#> 42 4.1 989.9185 10.08151
#> 43 4.2 989.9165 10.08350
#> 44 4.3 989.9145 10.08550
#> 45 4.4 989.9125 10.08750
#> 46 4.5 989.9105 10.08949
#> 47 4.6 989.9085 10.09149
#> 48 4.7 989.9065 10.09349
#> 49 4.8 989.9045 10.09549
#> 50 4.9 989.9025 10.09749
#> 51 5.0 989.9005 10.09949
#> 52 5.1 989.8985 10.10149
#> 53 5.2 989.8965 10.10349
#> 54 5.3 989.8945 10.10549
#> 55 5.4 989.8925 10.10749
#> 56 5.5 989.8905 10.10949
#> 57 5.6 989.8885 10.11149
#> 58 5.7 989.8865 10.11349
#> 59 5.8 989.8845 10.11550
#> 60 5.9 989.8825 10.11750
#> 61 6.0 989.8805 10.11950
#> 62 6.1 989.8785 10.12150
#> 63 6.2 989.8765 10.12351
#> 64 6.3 989.8745 10.12551
#> 65 6.4 989.8725 10.12752
#> 66 6.5 989.8705 10.12952
#> 67 6.6 989.8685 10.13153
#> 68 6.7 989.8665 10.13353
#> 69 6.8 989.8645 10.13554
#> 70 6.9 989.8625 10.13755
#> 71 7.0 989.8604 10.13956
#> 72 7.1 989.8584 10.14156
#> 73 7.2 989.8564 10.14357
#> 74 7.3 989.8544 10.14558
#> 75 7.4 989.8524 10.14759
#> 76 7.5 989.8504 10.14960
#> 77 7.6 989.8484 10.15161
#> 78 7.7 989.8464 10.15362
#> 79 7.8 989.8444 10.15563
#> 80 7.9 989.8424 10.15764
#> 81 8.0 989.8404 10.15965
#> 82 8.1 989.8383 10.16166
#> 83 8.2 989.8363 10.16367
#> 84 8.3 989.8343 10.16568
#> 85 8.4 989.8323 10.16770
#> 86 8.5 989.8303 10.16971
#> 87 8.6 989.8283 10.17172
#> 88 8.7 989.8263 10.17374
#> 89 8.8 989.8242 10.17575
#> 90 8.9 989.8222 10.17777
#> 91 9.0 989.8202 10.17978
#> 92 9.1 989.8182 10.18180
#> 93 9.2 989.8162 10.18381
#> 94 9.3 989.8142 10.18583
#> 95 9.4 989.8122 10.18784
#> 96 9.5 989.8101 10.18986
#> 97 9.6 989.8081 10.19188
#> 98 9.7 989.8061 10.19390
#> 99 9.8 989.8041 10.19592
#> 100 9.9 989.8021 10.19793
#> 101 10.0 989.8000 10.19995
#> 102 10.1 989.7980 10.20197
#> 103 10.2 989.7960 10.20399
#> 104 10.3 989.7940 10.20601
#> 105 10.4 989.7920 10.20803
#> 106 10.5 989.7899 10.21005
#> 107 10.6 989.7879 10.21208
#> 108 10.7 989.7859 10.21410
#> 109 10.8 989.7839 10.21612
#> 110 10.9 989.7819 10.21814
#> 111 11.0 989.7798 10.22016
#> 112 11.1 989.7778 10.22219
#> 113 11.2 989.7758 10.22421
#> 114 11.3 989.7738 10.22624
#> 115 11.4 989.7717 10.22826
#> 116 11.5 989.7697 10.23029
#> 117 11.6 989.7677 10.23231
#> 118 11.7 989.7657 10.23434
#> 119 11.8 989.7636 10.23636
#> 120 11.9 989.7616 10.23839
#> 121 12.0 989.7596 10.24042
#> 122 12.1 989.7576 10.24244
#> 123 12.2 989.7555 10.24447
#> 124 12.3 989.7535 10.24650
#> 125 12.4 989.7515 10.24853
#> 126 12.5 989.7494 10.25056
#> 127 12.6 989.7474 10.25259
#> 128 12.7 989.7454 10.25462
#> 129 12.8 989.7434 10.25665
#> 130 12.9 989.7413 10.25868
#> 131 13.0 989.7393 10.26071
#> 132 13.1 989.7373 10.26274
#> 133 13.2 989.7352 10.26477
#> 134 13.3 989.7332 10.26680
#> 135 13.4 989.7312 10.26883
#> 136 13.5 989.7291 10.27087
#> 137 13.6 989.7271 10.27290
#> 138 13.7 989.7251 10.27493
#> 139 13.8 989.7230 10.27697
#> 140 13.9 989.7210 10.27900
#> 141 14.0 989.7190 10.28104
#> 142 14.1 989.7169 10.28307
#> 143 14.2 989.7149 10.28511
#> 144 14.3 989.7129 10.28714
#> 145 14.4 989.7108 10.28918
#> 146 14.5 989.7088 10.29122
#> 147 14.6 989.7067 10.29326
#> 148 14.7 989.7047 10.29529
#> 149 14.8 989.7027 10.29733
#> 150 14.9 989.7006 10.29937
#> 151 15.0 989.6986 10.30141
#> 152 15.1 989.6966 10.30345
#> 153 15.2 989.6945 10.30549
#> 154 15.3 989.6925 10.30753
#> 155 15.4 989.6904 10.30957
#> 156 15.5 989.6884 10.31161
#> 157 15.6 989.6864 10.31365
#> 158 15.7 989.6843 10.31569
#> 159 15.8 989.6823 10.31773
#> 160 15.9 989.6802 10.31978
#> 161 16.0 989.6782 10.32182
#> 162 16.1 989.6761 10.32386
#> 163 16.2 989.6741 10.32591
#> 164 16.3 989.6721 10.32795
#> 165 16.4 989.6700 10.32999
#> 166 16.5 989.6680 10.33204
#> 167 16.6 989.6659 10.33408
#> 168 16.7 989.6639 10.33613
#> 169 16.8 989.6618 10.33818
#> 170 16.9 989.6598 10.34022
#> 171 17.0 989.6577 10.34227
#> 172 17.1 989.6557 10.34432
#> 173 17.2 989.6536 10.34636
#> 174 17.3 989.6516 10.34841
#> 175 17.4 989.6495 10.35046
#> 176 17.5 989.6475 10.35251
#> 177 17.6 989.6454 10.35456
#> 178 17.7 989.6434 10.35661
#> 179 17.8 989.6413 10.35866
#> 180 17.9 989.6393 10.36071
#> 181 18.0 989.6372 10.36276
#> 182 18.1 989.6352 10.36481
#> 183 18.2 989.6331 10.36686
#> 184 18.3 989.6311 10.36891
#> 185 18.4 989.6290 10.37097
#> 186 18.5 989.6270 10.37302
#> 187 18.6 989.6249 10.37507
#> 188 18.7 989.6229 10.37713
#> 189 18.8 989.6208 10.37918
#> 190 18.9 989.6188 10.38124
#> 191 19.0 989.6167 10.38329
#> 192 19.1 989.6147 10.38535
#> 193 19.2 989.6126 10.38740
#> 194 19.3 989.6105 10.38946
#> 195 19.4 989.6085 10.39151
#> 196 19.5 989.6064 10.39357
#> 197 19.6 989.6044 10.39563
#> 198 19.7 989.6023 10.39769
#> 199 19.8 989.6003 10.39974
#> 200 19.9 989.5982 10.40180
#> 201 20.0 989.5961 10.40386
#> 202 20.1 989.5941 10.40592
#> 203 20.2 989.5920 10.40798
#> 204 20.3 989.5900 10.41004
#> 205 20.4 989.5879 10.41210
#> 206 20.5 989.5858 10.41416
#> 207 20.6 989.5838 10.41622
#> 208 20.7 989.5817 10.41829
#> 209 20.8 989.5797 10.42035
#> 210 20.9 989.5776 10.42241
#> 211 21.0 989.5755 10.42447
#> 212 21.1 989.5735 10.42654
#> 213 21.2 989.5714 10.42860
#> 214 21.3 989.5693 10.43066
#> 215 21.4 989.5673 10.43273
#> 216 21.5 989.5652 10.43479
#> 217 21.6 989.5631 10.43686
#> 218 21.7 989.5611 10.43893
#> 219 21.8 989.5590 10.44099
#> 220 21.9 989.5569 10.44306
#> 221 22.0 989.5549 10.44513
#> 222 22.1 989.5528 10.44719
#> 223 22.2 989.5507 10.44926
#> 224 22.3 989.5487 10.45133
#> 225 22.4 989.5466 10.45340
#> 226 22.5 989.5445 10.45547
#> 227 22.6 989.5425 10.45754
#> 228 22.7 989.5404 10.45961
#> 229 22.8 989.5383 10.46168
#> 230 22.9 989.5363 10.46375
#> 231 23.0 989.5342 10.46582
#> 232 23.1 989.5321 10.46789
#> 233 23.2 989.5300 10.46996
#> 234 23.3 989.5280 10.47203
#> 235 23.4 989.5259 10.47411
#> 236 23.5 989.5238 10.47618
#> 237 23.6 989.5217 10.47825
#> 238 23.7 989.5197 10.48033
#> 239 23.8 989.5176 10.48240
#> 240 23.9 989.5155 10.48448
#> 241 24.0 989.5134 10.48655
#> 242 24.1 989.5114 10.48863
#> 243 24.2 989.5093 10.49070
#> 244 24.3 989.5072 10.49278
#> 245 24.4 989.5051 10.49485
#> 246 24.5 989.5031 10.49693
#> 247 24.6 989.5010 10.49901
#> 248 24.7 989.4989 10.50109
#> 249 24.8 989.4968 10.50317
#> 250 24.9 989.4948 10.50524
#> 251 25.0 989.4927 10.50732
#> 252 25.1 989.4906 10.50940
#> 253 25.2 989.4885 10.51148
#> 254 25.3 989.4864 10.51356
#> 255 25.4 989.4844 10.51564
#> 256 25.5 989.4823 10.51773
#> 257 25.6 989.4802 10.51981
#> 258 25.7 989.4781 10.52189
#> 259 25.8 989.4760 10.52397
#> 260 25.9 989.4739 10.52605
#> 261 26.0 989.4719 10.52814
#> 262 26.1 989.4698 10.53022
#> 263 26.2 989.4677 10.53231
#> 264 26.3 989.4656 10.53439
#> 265 26.4 989.4635 10.53648
#> 266 26.5 989.4614 10.53856
#> 267 26.6 989.4594 10.54065
#> 268 26.7 989.4573 10.54273
#> 269 26.8 989.4552 10.54482
#> 270 26.9 989.4531 10.54691
#> 271 27.0 989.4510 10.54899
#> 272 27.1 989.4489 10.55108
#> 273 27.2 989.4468 10.55317
#> 274 27.3 989.4447 10.55526
#> 275 27.4 989.4427 10.55735
#> 276 27.5 989.4406 10.55944
#> 277 27.6 989.4385 10.56153
#> 278 27.7 989.4364 10.56362
#> 279 27.8 989.4343 10.56571
#> 280 27.9 989.4322 10.56780
#> 281 28.0 989.4301 10.56989
#> 282 28.1 989.4280 10.57198
#> 283 28.2 989.4259 10.57407
#> 284 28.3 989.4238 10.57617
#> 285 28.4 989.4217 10.57826
#> 286 28.5 989.4196 10.58035
#> 287 28.6 989.4176 10.58245
#> 288 28.7 989.4155 10.58454
#> 289 28.8 989.4134 10.58664
#> 290 28.9 989.4113 10.58873
#> 291 29.0 989.4092 10.59083
#> 292 29.1 989.4071 10.59292
#> 293 29.2 989.4050 10.59502
#> 294 29.3 989.4029 10.59711
#> 295 29.4 989.4008 10.59921
#> 296 29.5 989.3987 10.60131
#> 297 29.6 989.3966 10.60341
#> 298 29.7 989.3945 10.60551
#> 299 29.8 989.3924 10.60760
#> 300 29.9 989.3903 10.60970
#> 301 30.0 989.3882 10.61180
# Open population with births and deaths
model_si(
init = c(S = 990, I = 10),
params = c(beta = 0.002, b = 0.01, d = 0.01),
times = seq(0, 200, by = 1)
)
#> time S I
#> 1 0 990.0000 10.000000
#> 2 1 990.0799 9.920121
#> 3 2 990.1591 9.840882
#> 4 3 990.2377 9.762277
#> 5 4 990.3157 9.684302
#> 6 5 990.3930 9.606952
#> 7 6 990.4698 9.530220
#> 8 7 990.5459 9.454103
#> 9 8 990.6214 9.378595
#> 10 9 990.6963 9.303692
#> 11 10 990.7706 9.229388
#> 12 11 990.8443 9.155680
#> 13 12 990.9174 9.082561
#> 14 13 990.9900 9.010027
#> 15 14 991.0619 8.938074
#> 16 15 991.1333 8.866697
#> 17 16 991.2041 8.795891
#> 18 17 991.2743 8.725652
#> 19 18 991.3440 8.655974
#> 20 19 991.4131 8.586855
#> 21 20 991.4817 8.518288
#> 22 21 991.5497 8.450270
#> 23 22 991.6172 8.382797
#> 24 23 991.6841 8.315863
#> 25 24 991.7505 8.249465
#> 26 25 991.8164 8.183598
#> 27 26 991.8817 8.118258
#> 28 27 991.9466 8.053441
#> 29 28 992.0109 7.989142
#> 30 29 992.0746 7.925358
#> 31 30 992.1379 7.862084
#> 32 31 992.2007 7.799316
#> 33 32 992.2629 7.737050
#> 34 33 992.3247 7.675282
#> 35 34 992.3860 7.614009
#> 36 35 992.4468 7.553225
#> 37 36 992.5071 7.492928
#> 38 37 992.5669 7.433112
#> 39 38 992.6262 7.373775
#> 40 39 992.6851 7.314913
#> 41 40 992.7435 7.256522
#> 42 41 992.8014 7.198597
#> 43 42 992.8589 7.141136
#> 44 43 992.9159 7.084134
#> 45 44 992.9724 7.027587
#> 46 45 993.0285 6.971493
#> 47 46 993.0842 6.915848
#> 48 47 993.1394 6.860647
#> 49 48 993.1941 6.805888
#> 50 49 993.2484 6.751567
#> 51 50 993.3023 6.697680
#> 52 51 993.3558 6.644223
#> 53 52 993.4088 6.591194
#> 54 53 993.4614 6.538589
#> 55 54 993.5136 6.486405
#> 56 55 993.5654 6.434637
#> 57 56 993.6167 6.383284
#> 58 57 993.6677 6.332341
#> 59 58 993.7182 6.281805
#> 60 59 993.7683 6.231673
#> 61 60 993.8181 6.181942
#> 62 61 993.8674 6.132608
#> 63 62 993.9163 6.083668
#> 64 63 993.9649 6.035120
#> 65 64 994.0130 5.986960
#> 66 65 994.0608 5.939184
#> 67 66 994.1082 5.891791
#> 68 67 994.1552 5.844776
#> 69 68 994.2019 5.798137
#> 70 69 994.2481 5.751870
#> 71 70 994.2940 5.705973
#> 72 71 994.3396 5.660443
#> 73 72 994.3847 5.615277
#> 74 73 994.4295 5.570472
#> 75 74 994.4740 5.526024
#> 76 75 994.5181 5.481932
#> 77 76 994.5618 5.438192
#> 78 77 994.6052 5.394802
#> 79 78 994.6482 5.351758
#> 80 79 994.6909 5.309058
#> 81 80 994.7333 5.266700
#> 82 81 994.7753 5.224679
#> 83 82 994.8170 5.182995
#> 84 83 994.8584 5.141643
#> 85 84 994.8994 5.100622
#> 86 85 994.9401 5.059928
#> 87 86 994.9804 5.019560
#> 88 87 995.0205 4.979514
#> 89 88 995.0602 4.939787
#> 90 89 995.0996 4.900379
#> 91 90 995.1387 4.861284
#> 92 91 995.1775 4.822503
#> 93 92 995.2160 4.784031
#> 94 93 995.2541 4.745866
#> 95 94 995.2920 4.708006
#> 96 95 995.3296 4.670448
#> 97 96 995.3668 4.633191
#> 98 97 995.4038 4.596230
#> 99 98 995.4404 4.559566
#> 100 99 995.4768 4.523193
#> 101 100 995.5129 4.487112
#> 102 101 995.5487 4.451318
#> 103 102 995.5842 4.415811
#> 104 103 995.6194 4.380587
#> 105 104 995.6544 4.345644
#> 106 105 995.6890 4.310980
#> 107 106 995.7234 4.276593
#> 108 107 995.7575 4.242481
#> 109 108 995.7914 4.208641
#> 110 109 995.8249 4.175071
#> 111 110 995.8582 4.141769
#> 112 111 995.8913 4.108733
#> 113 112 995.9240 4.075961
#> 114 113 995.9565 4.043451
#> 115 114 995.9888 4.011200
#> 116 115 996.0208 3.979206
#> 117 116 996.0525 3.947468
#> 118 117 996.0840 3.915984
#> 119 118 996.1152 3.884751
#> 120 119 996.1462 3.853767
#> 121 120 996.1770 3.823030
#> 122 121 996.2075 3.792539
#> 123 122 996.2377 3.762292
#> 124 123 996.2677 3.732285
#> 125 124 996.2975 3.702519
#> 126 125 996.3270 3.672990
#> 127 126 996.3563 3.643696
#> 128 127 996.3854 3.614637
#> 129 128 996.4142 3.585809
#> 130 129 996.4428 3.557212
#> 131 130 996.4712 3.528843
#> 132 131 996.4993 3.500700
#> 133 132 996.5272 3.472782
#> 134 133 996.5549 3.445086
#> 135 134 996.5824 3.417612
#> 136 135 996.6096 3.390357
#> 137 136 996.6367 3.363320
#> 138 137 996.6635 3.336498
#> 139 138 996.6901 3.309891
#> 140 139 996.7165 3.283496
#> 141 140 996.7427 3.257311
#> 142 141 996.7687 3.231336
#> 143 142 996.7944 3.205568
#> 144 143 996.8200 3.180005
#> 145 144 996.8454 3.154647
#> 146 145 996.8705 3.129490
#> 147 146 996.8955 3.104535
#> 148 147 996.9202 3.079779
#> 149 148 996.9448 3.055220
#> 150 149 996.9691 3.030857
#> 151 150 996.9933 3.006689
#> 152 151 997.0173 2.982714
#> 153 152 997.0411 2.958930
#> 154 153 997.0647 2.935335
#> 155 154 997.0881 2.911929
#> 156 155 997.1113 2.888710
#> 157 156 997.1343 2.865676
#> 158 157 997.1572 2.842826
#> 159 158 997.1798 2.820158
#> 160 159 997.2023 2.797671
#> 161 160 997.2246 2.775363
#> 162 161 997.2468 2.753234
#> 163 162 997.2687 2.731281
#> 164 163 997.2905 2.709503
#> 165 164 997.3121 2.687899
#> 166 165 997.3335 2.666467
#> 167 166 997.3548 2.645207
#> 168 167 997.3759 2.624116
#> 169 168 997.3968 2.603193
#> 170 169 997.4176 2.582437
#> 171 170 997.4382 2.561847
#> 172 171 997.4586 2.541421
#> 173 172 997.4788 2.521158
#> 174 173 997.4989 2.501056
#> 175 174 997.5189 2.481115
#> 176 175 997.5387 2.461333
#> 177 176 997.5583 2.441709
#> 178 177 997.5778 2.422242
#> 179 178 997.5971 2.402930
#> 180 179 997.6162 2.383771
#> 181 180 997.6352 2.364766
#> 182 181 997.6541 2.345912
#> 183 182 997.6728 2.327209
#> 184 183 997.6913 2.308655
#> 185 184 997.7098 2.290249
#> 186 185 997.7280 2.271990
#> 187 186 997.7461 2.253876
#> 188 187 997.7641 2.235907
#> 189 188 997.7819 2.218081
#> 190 189 997.7996 2.200398
#> 191 190 997.8171 2.182855
#> 192 191 997.8345 2.165452
#> 193 192 997.8518 2.148189
#> 194 193 997.8689 2.131063
#> 195 194 997.8859 2.114073
#> 196 195 997.9028 2.097219
#> 197 196 997.9195 2.080500
#> 198 197 997.9361 2.063914
#> 199 198 997.9525 2.047460
#> 200 199 997.9689 2.031137
#> 201 200 997.9851 2.014945