Two-compartment model with recovery but no lasting immunity.
Arguments
- init
Named numeric vector, e.g.
c(S = 990, I = 10).- params
Named numeric vector, e.g.
c(beta = 0.002, gamma = 0.1).- beta
Transmission rate.
- gamma
Recovery rate (1/gamma = mean infectious period).
- 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): $$\frac{dS}{dt} = -\beta \frac{S I}{N} + \gamma I$$ $$\frac{dI}{dt} = \beta \frac{S I}{N} - \gamma I$$
Open population (when b / d are provided):
$$\frac{dS}{dt} = b N - \beta \frac{S I}{N} + \gamma I - d S$$
$$\frac{dI}{dt} = \beta \frac{S I}{N} - \gamma I - d I$$
In the closed case population size \(N = S + I\) is conserved.
Examples
# Closed population
model_sis(
init = c(S = 990, I = 10),
params = c(beta = 0.002, gamma = 0.1),
times = seq(0, 50, by = 0.1)
)
#> time S I
#> 1 0.0 990.0000 10.00000000
#> 2 0.1 990.0975 9.90245815
#> 3 0.2 990.1941 9.80586793
#> 4 0.3 990.2898 9.71022006
#> 5 0.4 990.3845 9.61550647
#> 6 0.5 990.4783 9.52171652
#> 7 0.6 990.5712 9.42884158
#> 8 0.7 990.6631 9.33687271
#> 9 0.8 990.7542 9.24580107
#> 10 0.9 990.8444 9.15561791
#> 11 1.0 990.9337 9.06631455
#> 12 1.1 991.0221 8.97788241
#> 13 1.2 991.1097 8.89031299
#> 14 1.3 991.1964 8.80359787
#> 15 1.4 991.2823 8.71772871
#> 16 1.5 991.3673 8.63269725
#> 17 1.6 991.4515 8.54849532
#> 18 1.7 991.5349 8.46511483
#> 19 1.8 991.6175 8.38254775
#> 20 1.9 991.6992 8.30078615
#> 21 2.0 991.7802 8.21982217
#> 22 2.1 991.8604 8.13964803
#> 23 2.2 991.9397 8.06025601
#> 24 2.3 992.0184 7.98163849
#> 25 2.4 992.0962 7.90378791
#> 26 2.5 992.1733 7.82669678
#> 27 2.6 992.2496 7.75035769
#> 28 2.7 992.3252 7.67476331
#> 29 2.8 992.4001 7.59990636
#> 30 2.9 992.4742 7.52577965
#> 31 3.0 992.5476 7.45237606
#> 32 3.1 992.6203 7.37968853
#> 33 3.2 992.6923 7.30771006
#> 34 3.3 992.7636 7.23643375
#> 35 3.4 992.8341 7.16585274
#> 36 3.5 992.9040 7.09596025
#> 37 3.6 992.9733 7.02674955
#> 38 3.7 993.0418 6.95821400
#> 39 3.8 993.1097 6.89034701
#> 40 3.9 993.1769 6.82314204
#> 41 4.0 993.2434 6.75659266
#> 42 4.1 993.3093 6.69069245
#> 43 4.2 993.3746 6.62543508
#> 44 4.3 993.4392 6.56081428
#> 45 4.4 993.5032 6.49682384
#> 46 4.5 993.5665 6.43345761
#> 47 4.6 993.6293 6.37070949
#> 48 4.7 993.6914 6.30857347
#> 49 4.8 993.7530 6.24704355
#> 50 4.9 993.8139 6.18611384
#> 51 5.0 993.8742 6.12577847
#> 52 5.1 993.9340 6.06603165
#> 53 5.2 993.9931 6.00686763
#> 54 5.3 994.0517 5.94828073
#> 55 5.4 994.1097 5.89026531
#> 56 5.5 994.1672 5.83281580
#> 57 5.6 994.2241 5.77592668
#> 58 5.7 994.2804 5.71959248
#> 59 5.8 994.3362 5.66380778
#> 60 5.9 994.3914 5.60856723
#> 61 6.0 994.4461 5.55386552
#> 62 6.1 994.5003 5.49969739
#> 63 6.2 994.5539 5.44605763
#> 64 6.3 994.6071 5.39294108
#> 65 6.4 994.6597 5.34034266
#> 66 6.5 994.7117 5.28825728
#> 67 6.6 994.7633 5.23667997
#> 68 6.7 994.8144 5.18560574
#> 69 6.8 994.8650 5.13502971
#> 70 6.9 994.9151 5.08494700
#> 71 7.0 994.9646 5.03535281
#> 72 7.1 995.0138 4.98624236
#> 73 7.2 995.0624 4.93761095
#> 74 7.3 995.1105 4.88945389
#> 75 7.4 995.1582 4.84176655
#> 76 7.5 995.2055 4.79454437
#> 77 7.6 995.2522 4.74778278
#> 78 7.7 995.2985 4.70147732
#> 79 7.8 995.3444 4.65562351
#> 80 7.9 995.3898 4.61021696
#> 81 8.0 995.4347 4.56525331
#> 82 8.1 995.4793 4.52072823
#> 83 8.2 995.5234 4.47663744
#> 84 8.3 995.5670 4.43297671
#> 85 8.4 995.6103 4.38974185
#> 86 8.5 995.6531 4.34692869
#> 87 8.6 995.6955 4.30453312
#> 88 8.7 995.7374 4.26255108
#> 89 8.8 995.7790 4.22097851
#> 90 8.9 995.8202 4.17981144
#> 91 9.0 995.8610 4.13904591
#> 92 9.1 995.9013 4.09867799
#> 93 9.2 995.9413 4.05870381
#> 94 9.3 995.9809 4.01911953
#> 95 9.4 996.0201 3.97992135
#> 96 9.5 996.0589 3.94110549
#> 97 9.6 996.0973 3.90266823
#> 98 9.7 996.1354 3.86460588
#> 99 9.8 996.1731 3.82691477
#> 100 9.9 996.2104 3.78959129
#> 101 10.0 996.2474 3.75263185
#> 102 10.1 996.2840 3.71603289
#> 103 10.2 996.3202 3.67979091
#> 104 10.3 996.3561 3.64390242
#> 105 10.4 996.3916 3.60836397
#> 106 10.5 996.4268 3.57317214
#> 107 10.6 996.4617 3.53832357
#> 108 10.7 996.4962 3.50381488
#> 109 10.8 996.5304 3.46964278
#> 110 10.9 996.5642 3.43580398
#> 111 11.0 996.5977 3.40229523
#> 112 11.1 996.6309 3.36911330
#> 113 11.2 996.6637 3.33625501
#> 114 11.3 996.6963 3.30371720
#> 115 11.4 996.7285 3.27149675
#> 116 11.5 996.7604 3.23959055
#> 117 11.6 996.7920 3.20799556
#> 118 11.7 996.8233 3.17670872
#> 119 11.8 996.8543 3.14572703
#> 120 11.9 996.8850 3.11504752
#> 121 12.0 996.9153 3.08466724
#> 122 12.1 996.9454 3.05458327
#> 123 12.2 996.9752 3.02479272
#> 124 12.3 997.0047 2.99529272
#> 125 12.4 997.0339 2.96608045
#> 126 12.5 997.0628 2.93715310
#> 127 12.6 997.0915 2.90850788
#> 128 12.7 997.1199 2.88014205
#> 129 12.8 997.1479 2.85205287
#> 130 12.9 997.1758 2.82423766
#> 131 13.0 997.2033 2.79669374
#> 132 13.1 997.2306 2.76941846
#> 133 13.2 997.2576 2.74240920
#> 134 13.3 997.2843 2.71566337
#> 135 13.4 997.3108 2.68917840
#> 136 13.5 997.3370 2.66295174
#> 137 13.6 997.3630 2.63698087
#> 138 13.7 997.3887 2.61126330
#> 139 13.8 997.4142 2.58579656
#> 140 13.9 997.4394 2.56057820
#> 141 14.0 997.4644 2.53560580
#> 142 14.1 997.4891 2.51087696
#> 143 14.2 997.5136 2.48638930
#> 144 14.3 997.5379 2.46214048
#> 145 14.4 997.5619 2.43812815
#> 146 14.5 997.5856 2.41435002
#> 147 14.6 997.6092 2.39080380
#> 148 14.7 997.6325 2.36748723
#> 149 14.8 997.6556 2.34439807
#> 150 14.9 997.6785 2.32153410
#> 151 15.0 997.7011 2.29889312
#> 152 15.1 997.7235 2.27647295
#> 153 15.2 997.7457 2.25427146
#> 154 15.3 997.7677 2.23228649
#> 155 15.4 997.7895 2.21051595
#> 156 15.5 997.8110 2.18895773
#> 157 15.6 997.8324 2.16760977
#> 158 15.7 997.8535 2.14647002
#> 159 15.8 997.8745 2.12553645
#> 160 15.9 997.8952 2.10480703
#> 161 16.0 997.9157 2.08427979
#> 162 16.1 997.9360 2.06395276
#> 163 16.2 997.9562 2.04382397
#> 164 16.3 997.9761 2.02389150
#> 165 16.4 997.9958 2.00415342
#> 166 16.5 998.0154 1.98460785
#> 167 16.6 998.0347 1.96525291
#> 168 16.7 998.0539 1.94608673
#> 169 16.8 998.0729 1.92710748
#> 170 16.9 998.0917 1.90831334
#> 171 17.0 998.1103 1.88970249
#> 172 17.1 998.1287 1.87127315
#> 173 17.2 998.1470 1.85302355
#> 174 17.3 998.1650 1.83495193
#> 175 17.4 998.1829 1.81705657
#> 176 17.5 998.2007 1.79933573
#> 177 17.6 998.2182 1.78178773
#> 178 17.7 998.2356 1.76441086
#> 179 17.8 998.2528 1.74720347
#> 180 17.9 998.2698 1.73016390
#> 181 18.0 998.2867 1.71329052
#> 182 18.1 998.3034 1.69658170
#> 183 18.2 998.3200 1.68003584
#> 184 18.3 998.3363 1.66365134
#> 185 18.4 998.3526 1.64742664
#> 186 18.5 998.3686 1.63136018
#> 187 18.6 998.3845 1.61545040
#> 188 18.7 998.4003 1.59969580
#> 189 18.8 998.4159 1.58409484
#> 190 18.9 998.4314 1.56864604
#> 191 19.0 998.4467 1.55334790
#> 192 19.1 998.4618 1.53819897
#> 193 19.2 998.4768 1.52319777
#> 194 19.3 998.4917 1.50834288
#> 195 19.4 998.5064 1.49363287
#> 196 19.5 998.5209 1.47906632
#> 197 19.6 998.5354 1.46464183
#> 198 19.7 998.5496 1.45035802
#> 199 19.8 998.5638 1.43621352
#> 200 19.9 998.5778 1.42220696
#> 201 20.0 998.5917 1.40833700
#> 202 20.1 998.6054 1.39460232
#> 203 20.2 998.6190 1.38100158
#> 204 20.3 998.6325 1.36753349
#> 205 20.4 998.6458 1.35419675
#> 206 20.5 998.6590 1.34099008
#> 207 20.6 998.6721 1.32791220
#> 208 20.7 998.6850 1.31496188
#> 209 20.8 998.6979 1.30213785
#> 210 20.9 998.7106 1.28943889
#> 211 21.0 998.7231 1.27686378
#> 212 21.1 998.7356 1.26441130
#> 213 21.2 998.7479 1.25208028
#> 214 21.3 998.7601 1.23986951
#> 215 21.4 998.7722 1.22777783
#> 216 21.5 998.7842 1.21580408
#> 217 21.6 998.7961 1.20394710
#> 218 21.7 998.8078 1.19220576
#> 219 21.8 998.8194 1.18057892
#> 220 21.9 998.8309 1.16906548
#> 221 22.0 998.8423 1.15766433
#> 222 22.1 998.8536 1.14637436
#> 223 22.2 998.8648 1.13519450
#> 224 22.3 998.8759 1.12412368
#> 225 22.4 998.8868 1.11316082
#> 226 22.5 998.8977 1.10230488
#> 227 22.6 998.9084 1.09155481
#> 228 22.7 998.9191 1.08090959
#> 229 22.8 998.9296 1.07036818
#> 230 22.9 998.9401 1.05992958
#> 231 23.0 998.9504 1.04959278
#> 232 23.1 998.9606 1.03935679
#> 233 23.2 998.9708 1.02922063
#> 234 23.3 998.9808 1.01918332
#> 235 23.4 998.9908 1.00924390
#> 236 23.5 999.0006 0.99940141
#> 237 23.6 999.0103 0.98965492
#> 238 23.7 999.0200 0.98000347
#> 239 23.8 999.0296 0.97044616
#> 240 23.9 999.0390 0.96098205
#> 241 24.0 999.0484 0.95161024
#> 242 24.1 999.0577 0.94232983
#> 243 24.2 999.0669 0.93313992
#> 244 24.3 999.0760 0.92403964
#> 245 24.4 999.0850 0.91502811
#> 246 24.5 999.0939 0.90610447
#> 247 24.6 999.1027 0.89726785
#> 248 24.7 999.1115 0.88851742
#> 249 24.8 999.1201 0.87985232
#> 250 24.9 999.1287 0.87127173
#> 251 25.0 999.1372 0.86277482
#> 252 25.1 999.1456 0.85436077
#> 253 25.2 999.1540 0.84602878
#> 254 25.3 999.1622 0.83777805
#> 255 25.4 999.1704 0.82960779
#> 256 25.5 999.1785 0.82151721
#> 257 25.6 999.1865 0.81350553
#> 258 25.7 999.1944 0.80557198
#> 259 25.8 999.2023 0.79771580
#> 260 25.9 999.2101 0.78993624
#> 261 26.0 999.2178 0.78223255
#> 262 26.1 999.2254 0.77460400
#> 263 26.2 999.2330 0.76704983
#> 264 26.3 999.2404 0.75956934
#> 265 26.4 999.2478 0.75216181
#> 266 26.5 999.2552 0.74482651
#> 267 26.6 999.2624 0.73756275
#> 268 26.7 999.2696 0.73036983
#> 269 26.8 999.2768 0.72324706
#> 270 26.9 999.2838 0.71619375
#> 271 27.0 999.2908 0.70920923
#> 272 27.1 999.2977 0.70229283
#> 273 27.2 999.3046 0.69544387
#> 274 27.3 999.3113 0.68866172
#> 275 27.4 999.3181 0.68194570
#> 276 27.5 999.3247 0.67529518
#> 277 27.6 999.3313 0.66870952
#> 278 27.7 999.3378 0.66218808
#> 279 27.8 999.3443 0.65573025
#> 280 27.9 999.3507 0.64933539
#> 281 28.0 999.3570 0.64300290
#> 282 28.1 999.3633 0.63673217
#> 283 28.2 999.3695 0.63052259
#> 284 28.3 999.3756 0.62437357
#> 285 28.4 999.3817 0.61828452
#> 286 28.5 999.3877 0.61225485
#> 287 28.6 999.3937 0.60628398
#> 288 28.7 999.3996 0.60037134
#> 289 28.8 999.4055 0.59451637
#> 290 28.9 999.4113 0.58871849
#> 291 29.0 999.4170 0.58297716
#> 292 29.1 999.4227 0.57729182
#> 293 29.2 999.4283 0.57166193
#> 294 29.3 999.4339 0.56608694
#> 295 29.4 999.4394 0.56056632
#> 296 29.5 999.4449 0.55509954
#> 297 29.6 999.4503 0.54968607
#> 298 29.7 999.4557 0.54432540
#> 299 29.8 999.4610 0.53901700
#> 300 29.9 999.4662 0.53376038
#> 301 30.0 999.4714 0.52855502
#> 302 30.1 999.4766 0.52340042
#> 303 30.2 999.4817 0.51829610
#> 304 30.3 999.4868 0.51324155
#> 305 30.4 999.4918 0.50823630
#> 306 30.5 999.4967 0.50327986
#> 307 30.6 999.5016 0.49837175
#> 308 30.7 999.5065 0.49351151
#> 309 30.8 999.5113 0.48869867
#> 310 30.9 999.5161 0.48393277
#> 311 31.0 999.5208 0.47921335
#> 312 31.1 999.5255 0.47453995
#> 313 31.2 999.5301 0.46991212
#> 314 31.3 999.5347 0.46532943
#> 315 31.4 999.5392 0.46079143
#> 316 31.5 999.5437 0.45629769
#> 317 31.6 999.5482 0.45184777
#> 318 31.7 999.5526 0.44744125
#> 319 31.8 999.5569 0.44307770
#> 320 31.9 999.5612 0.43875671
#> 321 32.0 999.5655 0.43447786
#> 322 32.1 999.5698 0.43024073
#> 323 32.2 999.5740 0.42604493
#> 324 32.3 999.5781 0.42189005
#> 325 32.4 999.5822 0.41777568
#> 326 32.5 999.5863 0.41370144
#> 327 32.6 999.5903 0.40966694
#> 328 32.7 999.5943 0.40567177
#> 329 32.8 999.5983 0.40171558
#> 330 32.9 999.6022 0.39779796
#> 331 33.0 999.6061 0.39391855
#> 332 33.1 999.6099 0.39007697
#> 333 33.2 999.6137 0.38627286
#> 334 33.3 999.6175 0.38250584
#> 335 33.4 999.6212 0.37877556
#> 336 33.5 999.6249 0.37508166
#> 337 33.6 999.6286 0.37142379
#> 338 33.7 999.6322 0.36780159
#> 339 33.8 999.6358 0.36421471
#> 340 33.9 999.6393 0.36066281
#> 341 34.0 999.6429 0.35714555
#> 342 34.1 999.6463 0.35366259
#> 343 34.2 999.6498 0.35021360
#> 344 34.3 999.6532 0.34679825
#> 345 34.4 999.6566 0.34341620
#> 346 34.5 999.6599 0.34006714
#> 347 34.6 999.6632 0.33675073
#> 348 34.7 999.6665 0.33346667
#> 349 34.8 999.6698 0.33021464
#> 350 34.9 999.6730 0.32699432
#> 351 35.0 999.6762 0.32380540
#> 352 35.1 999.6794 0.32064759
#> 353 35.2 999.6825 0.31752057
#> 354 35.3 999.6856 0.31442404
#> 355 35.4 999.6886 0.31135772
#> 356 35.5 999.6917 0.30832130
#> 357 35.6 999.6947 0.30531449
#> 358 35.7 999.6977 0.30233700
#> 359 35.8 999.7006 0.29938855
#> 360 35.9 999.7035 0.29646885
#> 361 36.0 999.7064 0.29357763
#> 362 36.1 999.7093 0.29071461
#> 363 36.2 999.7121 0.28787950
#> 364 36.3 999.7149 0.28507204
#> 365 36.4 999.7177 0.28229197
#> 366 36.5 999.7205 0.27953900
#> 367 36.6 999.7232 0.27681288
#> 368 36.7 999.7259 0.27411335
#> 369 36.8 999.7286 0.27144015
#> 370 36.9 999.7312 0.26879301
#> 371 37.0 999.7338 0.26617169
#> 372 37.1 999.7364 0.26357593
#> 373 37.2 999.7390 0.26100549
#> 374 37.3 999.7415 0.25846012
#> 375 37.4 999.7441 0.25593956
#> 376 37.5 999.7466 0.25344359
#> 377 37.6 999.7490 0.25097196
#> 378 37.7 999.7515 0.24852444
#> 379 37.8 999.7539 0.24610078
#> 380 37.9 999.7563 0.24370076
#> 381 38.0 999.7587 0.24132415
#> 382 38.1 999.7610 0.23897071
#> 383 38.2 999.7634 0.23664022
#> 384 38.3 999.7657 0.23433247
#> 385 38.4 999.7680 0.23204721
#> 386 38.5 999.7702 0.22978425
#> 387 38.6 999.7725 0.22754335
#> 388 38.7 999.7747 0.22532430
#> 389 38.8 999.7769 0.22312690
#> 390 38.9 999.7790 0.22095093
#> 391 39.0 999.7812 0.21879617
#> 392 39.1 999.7833 0.21666243
#> 393 39.2 999.7855 0.21454950
#> 394 39.3 999.7875 0.21245718
#> 395 39.4 999.7896 0.21038526
#> 396 39.5 999.7917 0.20833354
#> 397 39.6 999.7937 0.20630184
#> 398 39.7 999.7957 0.20428995
#> 399 39.8 999.7977 0.20229767
#> 400 39.9 999.7997 0.20032483
#> 401 40.0 999.8016 0.19837123
#> 402 40.1 999.8036 0.19643668
#> 403 40.2 999.8055 0.19452099
#> 404 40.3 999.8074 0.19262399
#> 405 40.4 999.8093 0.19074549
#> 406 40.5 999.8111 0.18888530
#> 407 40.6 999.8130 0.18704326
#> 408 40.7 999.8148 0.18521918
#> 409 40.8 999.8166 0.18341289
#> 410 40.9 999.8184 0.18162422
#> 411 41.0 999.8201 0.17985299
#> 412 41.1 999.8219 0.17809903
#> 413 41.2 999.8236 0.17636218
#> 414 41.3 999.8254 0.17464226
#> 415 41.4 999.8271 0.17293912
#> 416 41.5 999.8287 0.17125259
#> 417 41.6 999.8304 0.16958251
#> 418 41.7 999.8321 0.16792871
#> 419 41.8 999.8337 0.16629104
#> 420 41.9 999.8353 0.16466934
#> 421 42.0 999.8369 0.16306346
#> 422 42.1 999.8385 0.16147324
#> 423 42.2 999.8401 0.15989852
#> 424 42.3 999.8417 0.15833917
#> 425 42.4 999.8432 0.15679502
#> 426 42.5 999.8447 0.15526592
#> 427 42.6 999.8462 0.15375174
#> 428 42.7 999.8477 0.15225233
#> 429 42.8 999.8492 0.15076754
#> 430 42.9 999.8507 0.14929723
#> 431 43.0 999.8522 0.14784126
#> 432 43.1 999.8536 0.14639949
#> 433 43.2 999.8550 0.14497178
#> 434 43.3 999.8564 0.14355799
#> 435 43.4 999.8578 0.14215799
#> 436 43.5 999.8592 0.14077164
#> 437 43.6 999.8606 0.13939881
#> 438 43.7 999.8620 0.13803937
#> 439 43.8 999.8633 0.13669319
#> 440 43.9 999.8646 0.13536013
#> 441 44.0 999.8660 0.13404008
#> 442 44.1 999.8673 0.13273290
#> 443 44.2 999.8686 0.13143847
#> 444 44.3 999.8698 0.13015666
#> 445 44.4 999.8711 0.12888735
#> 446 44.5 999.8724 0.12763042
#> 447 44.6 999.8736 0.12638574
#> 448 44.7 999.8748 0.12515321
#> 449 44.8 999.8761 0.12393270
#> 450 44.9 999.8773 0.12272408
#> 451 45.0 999.8785 0.12152726
#> 452 45.1 999.8797 0.12034211
#> 453 45.2 999.8808 0.11916851
#> 454 45.3 999.8820 0.11800636
#> 455 45.4 999.8831 0.11685554
#> 456 45.5 999.8843 0.11571595
#> 457 45.6 999.8854 0.11458747
#> 458 45.7 999.8865 0.11346999
#> 459 45.8 999.8876 0.11236342
#> 460 45.9 999.8887 0.11126763
#> 461 46.0 999.8898 0.11018253
#> 462 46.1 999.8909 0.10910801
#> 463 46.2 999.8920 0.10804398
#> 464 46.3 999.8930 0.10699031
#> 465 46.4 999.8941 0.10594693
#> 466 46.5 999.8951 0.10491372
#> 467 46.6 999.8961 0.10389058
#> 468 46.7 999.8971 0.10287742
#> 469 46.8 999.8981 0.10187415
#> 470 46.9 999.8991 0.10088065
#> 471 47.0 999.9001 0.09989685
#> 472 47.1 999.9011 0.09892264
#> 473 47.2 999.9020 0.09795793
#> 474 47.3 999.9030 0.09700263
#> 475 47.4 999.9039 0.09605665
#> 476 47.5 999.9049 0.09511989
#> 477 47.6 999.9058 0.09419226
#> 478 47.7 999.9067 0.09327368
#> 479 47.8 999.9076 0.09236407
#> 480 47.9 999.9085 0.09146332
#> 481 48.0 999.9094 0.09057135
#> 482 48.1 999.9103 0.08968809
#> 483 48.2 999.9112 0.08881343
#> 484 48.3 999.9121 0.08794731
#> 485 48.4 999.9129 0.08708964
#> 486 48.5 999.9138 0.08624033
#> 487 48.6 999.9146 0.08539930
#> 488 48.7 999.9154 0.08456647
#> 489 48.8 999.9163 0.08374176
#> 490 48.9 999.9171 0.08292510
#> 491 49.0 999.9179 0.08211640
#> 492 49.1 999.9187 0.08131559
#> 493 49.2 999.9195 0.08052259
#> 494 49.3 999.9203 0.07973732
#> 495 49.4 999.9210 0.07895971
#> 496 49.5 999.9218 0.07818968
#> 497 49.6 999.9226 0.07742717
#> 498 49.7 999.9233 0.07667208
#> 499 49.8 999.9241 0.07592437
#> 500 49.9 999.9248 0.07518394
#> 501 50.0 999.9255 0.07445074
# Open population with births and deaths
model_sis(
init = c(S = 990, I = 10),
params = c(beta = 0.3, gamma = 0.1, b = 0.01, d = 0.01),
times = seq(0, 200, by = 1)
)
#> time S I
#> 1 0 990.0000 10.00000
#> 2 1 987.9473 12.05267
#> 3 2 985.4831 14.51689
#> 4 3 982.5293 17.47074
#> 5 4 978.9948 21.00525
#> 6 5 974.7745 25.22552
#> 7 6 969.7482 30.25181
#> 8 7 963.7800 36.21995
#> 9 8 956.7190 43.28101
#> 10 9 948.4003 51.59965
#> 11 10 938.6491 61.35090
#> 12 11 927.2854 72.71459
#> 13 12 914.1329 85.86713
#> 14 13 899.0298 100.97024
#> 15 14 881.8435 118.15655
#> 16 15 862.4874 137.51256
#> 17 16 840.9396 159.06040
#> 18 17 817.2597 182.74029
#> 19 18 791.6035 208.39646
#> 20 19 764.2301 235.76992
#> 21 20 735.4991 264.50087
#> 22 21 705.8574 294.14256
#> 23 22 675.8137 324.18634
#> 24 23 645.9047 354.09528
#> 25 24 616.6580 383.34201
#> 26 25 588.5550 411.44504
#> 27 26 562.0013 437.99866
#> 28 27 537.3075 462.69250
#> 29 28 514.6805 485.31953
#> 30 29 494.2266 505.77340
#> 31 30 475.9627 524.03732
#> 32 31 459.8321 540.16791
#> 33 32 445.7230 554.27699
#> 34 33 433.4863 566.51368
#> 35 34 422.9514 577.04864
#> 36 35 413.9388 586.06123
#> 37 36 406.2703 593.72972
#> 38 37 399.7755 600.22450
#> 39 38 394.2963 605.70374
#> 40 39 389.6890 610.31099
#> 41 40 385.8257 614.17428
#> 42 41 382.5938 617.40620
#> 43 42 379.8953 620.10468
#> 44 43 377.6459 622.35409
#> 45 44 375.7734 624.22663
#> 46 45 374.2163 625.78368
#> 47 46 372.9228 627.07717
#> 48 47 371.8491 628.15088
#> 49 48 370.9584 629.04158
#> 50 49 370.2199 629.78006
#> 51 50 369.6079 630.39207
#> 52 51 369.1009 630.89907
#> 53 52 368.6810 631.31896
#> 54 53 368.3334 631.66661
#> 55 54 368.0456 631.95439
#> 56 55 367.8074 632.19257
#> 57 56 367.6103 632.38968
#> 58 57 367.4472 632.55277
#> 59 58 367.3123 632.68770
#> 60 59 367.2007 632.79932
#> 61 60 367.1083 632.89167
#> 62 61 367.0320 632.96805
#> 63 62 366.9688 633.03123
#> 64 63 366.9165 633.08349
#> 65 64 366.8733 633.12671
#> 66 65 366.8375 633.16245
#> 67 66 366.8080 633.19202
#> 68 67 366.7835 633.21647
#> 69 68 366.7633 633.23669
#> 70 69 366.7466 633.25341
#> 71 70 366.7328 633.26724
#> 72 71 366.7213 633.27867
#> 73 72 366.7119 633.28813
#> 74 73 366.7040 633.29595
#> 75 74 366.6976 633.30242
#> 76 75 366.6922 633.30777
#> 77 76 366.6878 633.31219
#> 78 77 366.6841 633.31585
#> 79 78 366.6811 633.31888
#> 80 79 366.6786 633.32138
#> 81 80 366.6766 633.32344
#> 82 81 366.6748 633.32516
#> 83 82 366.6734 633.32657
#> 84 83 366.6723 633.32774
#> 85 84 366.6713 633.32871
#> 86 85 366.6705 633.32951
#> 87 86 366.6698 633.33017
#> 88 87 366.6693 633.33072
#> 89 88 366.6688 633.33118
#> 90 89 366.6685 633.33155
#> 91 90 366.6681 633.33186
#> 92 91 366.6679 633.33211
#> 93 92 366.6677 633.33233
#> 94 93 366.6675 633.33250
#> 95 94 366.6674 633.33265
#> 96 95 366.6672 633.33276
#> 97 96 366.6671 633.33286
#> 98 97 366.6671 633.33294
#> 99 98 366.6670 633.33301
#> 100 99 366.6669 633.33307
#> 101 100 366.6669 633.33311
#> 102 101 366.6668 633.33315
#> 103 102 366.6668 633.33318
#> 104 103 366.6668 633.33321
#> 105 104 366.6668 633.33323
#> 106 105 366.6668 633.33325
#> 107 106 366.6667 633.33326
#> 108 107 366.6667 633.33328
#> 109 108 366.6667 633.33329
#> 110 109 366.6667 633.33329
#> 111 110 366.6667 633.33330
#> 112 111 366.6667 633.33331
#> 113 112 366.6667 633.33331
#> 114 113 366.6667 633.33331
#> 115 114 366.6667 633.33332
#> 116 115 366.6667 633.33332
#> 117 116 366.6667 633.33332
#> 118 117 366.6667 633.33332
#> 119 118 366.6667 633.33333
#> 120 119 366.6667 633.33333
#> 121 120 366.6667 633.33333
#> 122 121 366.6667 633.33333
#> 123 122 366.6667 633.33333
#> 124 123 366.6667 633.33333
#> 125 124 366.6667 633.33333
#> 126 125 366.6667 633.33333
#> 127 126 366.6667 633.33333
#> 128 127 366.6667 633.33333
#> 129 128 366.6667 633.33333
#> 130 129 366.6667 633.33333
#> 131 130 366.6667 633.33333
#> 132 131 366.6667 633.33333
#> 133 132 366.6667 633.33333
#> 134 133 366.6667 633.33333
#> 135 134 366.6667 633.33333
#> 136 135 366.6667 633.33333
#> 137 136 366.6667 633.33333
#> 138 137 366.6667 633.33333
#> 139 138 366.6667 633.33333
#> 140 139 366.6667 633.33333
#> 141 140 366.6667 633.33333
#> 142 141 366.6667 633.33333
#> 143 142 366.6667 633.33333
#> 144 143 366.6667 633.33333
#> 145 144 366.6667 633.33333
#> 146 145 366.6667 633.33333
#> 147 146 366.6667 633.33333
#> 148 147 366.6667 633.33333
#> 149 148 366.6667 633.33333
#> 150 149 366.6667 633.33333
#> 151 150 366.6667 633.33333
#> 152 151 366.6667 633.33333
#> 153 152 366.6667 633.33333
#> 154 153 366.6667 633.33333
#> 155 154 366.6667 633.33333
#> 156 155 366.6667 633.33333
#> 157 156 366.6667 633.33333
#> 158 157 366.6667 633.33333
#> 159 158 366.6667 633.33333
#> 160 159 366.6667 633.33333
#> 161 160 366.6667 633.33333
#> 162 161 366.6667 633.33333
#> 163 162 366.6667 633.33333
#> 164 163 366.6667 633.33333
#> 165 164 366.6667 633.33333
#> 166 165 366.6667 633.33333
#> 167 166 366.6667 633.33333
#> 168 167 366.6667 633.33333
#> 169 168 366.6667 633.33333
#> 170 169 366.6667 633.33333
#> 171 170 366.6667 633.33333
#> 172 171 366.6667 633.33333
#> 173 172 366.6667 633.33333
#> 174 173 366.6667 633.33333
#> 175 174 366.6667 633.33333
#> 176 175 366.6667 633.33333
#> 177 176 366.6667 633.33333
#> 178 177 366.6667 633.33333
#> 179 178 366.6667 633.33333
#> 180 179 366.6667 633.33333
#> 181 180 366.6667 633.33333
#> 182 181 366.6667 633.33333
#> 183 182 366.6667 633.33333
#> 184 183 366.6667 633.33333
#> 185 184 366.6667 633.33333
#> 186 185 366.6667 633.33333
#> 187 186 366.6667 633.33333
#> 188 187 366.6667 633.33333
#> 189 188 366.6667 633.33333
#> 190 189 366.6667 633.33333
#> 191 190 366.6667 633.33333
#> 192 191 366.6667 633.33333
#> 193 192 366.6667 633.33333
#> 194 193 366.6667 633.33333
#> 195 194 366.6667 633.33333
#> 196 195 366.6667 633.33333
#> 197 196 366.6667 633.33333
#> 198 197 366.6667 633.33333
#> 199 198 366.6667 633.33333
#> 200 199 366.6667 633.33333
#> 201 200 366.6667 633.33333