Four-compartment model that adds an exposed (latent) class.
Arguments
- init
Named numeric vector.
Rdefaults to 0 if omitted, e.g.c(S = 980, E = 10, I = 10).- params
Named numeric vector, e.g.
c(beta = 0.3, alpha = 0.2, gamma = 0.1).- beta
Transmission rate.
- alpha
Rate of progression from exposed to infectious (1/alpha = mean latent period).
- 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): $$\frac{dS}{dt} = -\beta \frac{S I}{N}$$ $$\frac{dE}{dt} = \beta \frac{S I}{N} - \alpha E$$ $$\frac{dI}{dt} = \alpha E - \gamma I$$ $$\frac{dR}{dt} = \gamma I$$
Open population (when b / d are provided):
$$\frac{dS}{dt} = b N - \beta \frac{S I}{N} - d S$$
$$\frac{dE}{dt} = \beta \frac{S I}{N} - \alpha E - d E$$
$$\frac{dI}{dt} = \alpha E - \gamma I - d I$$
$$\frac{dR}{dt} = \gamma I - d R$$
S Susceptible — not yet infected.
E Exposed — infected but not yet infectious (mean latent period \(1/\alpha\)).
I Infectious — actively spreading the pathogen (mean infectious period \(1/\gamma\)).
R Recovered — permanently immune.
In the closed case population size \(N = S + E + I + R\) is conserved.
Examples
# Closed population
model_seir(
init = c(S = 980, E = 10, I = 10),
params = c(beta = 0.3, alpha = 0.2, gamma = 0.1),
times = seq(0, 50, by = 0.1)
)
#> time S E I R
#> 1 0.0 980.0000 10.00000 10.00000 0.0000000
#> 2 0.1 979.7046 10.09449 10.10044 0.1005019
#> 3 0.2 979.4063 10.18995 10.20178 0.2020127
#> 4 0.3 979.1051 10.28639 10.30401 0.3045409
#> 5 0.4 978.8009 10.38382 10.40715 0.4080959
#> 6 0.5 978.4939 10.48223 10.51122 0.5126870
#> 7 0.6 978.1838 10.58164 10.61622 0.6183234
#> 8 0.7 977.8708 10.68205 10.72217 0.7250146
#> 9 0.8 977.5547 10.78345 10.82906 0.8327699
#> 10 0.9 977.2356 10.88587 10.93693 0.9415991
#> 11 1.0 976.9134 10.98930 11.04576 1.0515117
#> 12 1.1 976.5882 11.09374 11.15559 1.1625176
#> 13 1.2 976.2598 11.19921 11.26641 1.2746268
#> 14 1.3 975.9282 11.30571 11.37823 1.3878491
#> 15 1.4 975.5935 11.41325 11.49107 1.5021948
#> 16 1.5 975.2556 11.52182 11.60494 1.6176740
#> 17 1.6 974.9144 11.63144 11.71985 1.7342971
#> 18 1.7 974.5700 11.74212 11.83581 1.8520745
#> 19 1.8 974.2223 11.85385 11.95282 1.9710168
#> 20 1.9 973.8713 11.96665 12.07091 2.0911345
#> 21 2.0 973.5170 12.08052 12.19007 2.2124385
#> 22 2.1 973.1593 12.19546 12.31033 2.3349396
#> 23 2.2 972.7982 12.31150 12.43169 2.4586488
#> 24 2.3 972.4336 12.42862 12.55416 2.5835771
#> 25 2.4 972.0657 12.54684 12.67775 2.7097358
#> 26 2.5 971.6942 12.66616 12.80248 2.8371360
#> 27 2.6 971.3193 12.78660 12.92836 2.9657892
#> 28 2.7 970.9408 12.90816 13.05538 3.0957070
#> 29 2.8 970.5587 13.03084 13.18358 3.2269008
#> 30 2.9 970.1730 13.15465 13.31295 3.3593824
#> 31 3.0 969.7837 13.27961 13.44351 3.4931637
#> 32 3.1 969.3908 13.40571 13.57527 3.6282566
#> 33 3.2 968.9941 13.53296 13.70823 3.7646731
#> 34 3.3 968.5938 13.66138 13.84242 3.9024254
#> 35 3.4 968.1897 13.79097 13.97785 4.0415257
#> 36 3.5 967.7818 13.92174 14.11451 4.1819864
#> 37 3.6 967.3701 14.05369 14.25243 4.3238201
#> 38 3.7 966.9545 14.18684 14.39161 4.4670392
#> 39 3.8 966.5351 14.32118 14.53207 4.6116566
#> 40 3.9 966.1118 14.45674 14.67382 4.7576850
#> 41 4.0 965.6845 14.59351 14.81687 4.9051373
#> 42 4.1 965.2532 14.73150 14.96123 5.0540267
#> 43 4.2 964.8180 14.87073 15.10691 5.2043663
#> 44 4.3 964.3787 15.01120 15.25392 5.3561694
#> 45 4.4 963.9353 15.15292 15.40228 5.5094493
#> 46 4.5 963.4879 15.29590 15.55200 5.6642195
#> 47 4.6 963.0363 15.44014 15.70308 5.8204938
#> 48 4.7 962.5805 15.58565 15.85555 5.9782858
#> 49 4.8 962.1205 15.73245 16.00940 6.1376094
#> 50 4.9 961.6563 15.88054 16.16466 6.2984785
#> 51 5.0 961.1878 16.02992 16.32133 6.4609073
#> 52 5.1 960.7150 16.18061 16.47943 6.6249100
#> 53 5.2 960.2379 16.33262 16.63897 6.7905008
#> 54 5.3 959.7564 16.48595 16.79996 6.9576943
#> 55 5.4 959.2705 16.64062 16.96242 7.1265049
#> 56 5.5 958.7801 16.79663 17.12634 7.2969475
#> 57 5.6 958.2852 16.95398 17.29176 7.4690368
#> 58 5.7 957.7858 17.11270 17.45867 7.6427877
#> 59 5.8 957.2819 17.27278 17.62710 7.8182153
#> 60 5.9 956.7734 17.43423 17.79705 7.9953347
#> 61 6.0 956.2602 17.59707 17.96853 8.1741613
#> 62 6.1 955.7424 17.76131 18.14156 8.3547105
#> 63 6.2 955.2199 17.92694 18.31616 8.5369978
#> 64 6.3 954.6926 18.09399 18.49232 8.7210388
#> 65 6.4 954.1606 18.26246 18.67007 8.9068495
#> 66 6.5 953.6238 18.43235 18.84942 9.0944456
#> 67 6.6 953.0821 18.60368 19.03038 9.2838433
#> 68 6.7 952.5355 18.77646 19.21297 9.4750587
#> 69 6.8 951.9840 18.95069 19.39719 9.6681080
#> 70 6.9 951.4276 19.12638 19.58305 9.8630079
#> 71 7.0 950.8661 19.30355 19.77058 10.0597747
#> 72 7.1 950.2996 19.48219 19.95979 10.2584251
#> 73 7.2 949.7280 19.66233 20.15068 10.4589761
#> 74 7.3 949.1513 19.84396 20.34327 10.6614444
#> 75 7.4 948.5695 20.02710 20.53758 10.8658472
#> 76 7.5 947.9824 20.21176 20.73361 11.0722017
#> 77 7.6 947.3902 20.39794 20.93138 11.2805252
#> 78 7.7 946.7926 20.58566 21.13090 11.4908351
#> 79 7.8 946.1897 20.77491 21.33219 11.7031492
#> 80 7.9 945.5815 20.96572 21.53526 11.9174849
#> 81 8.0 944.9679 21.15809 21.74012 12.1338603
#> 82 8.1 944.3489 21.35202 21.94679 12.3522934
#> 83 8.2 943.7244 21.54754 22.15527 12.5728021
#> 84 8.3 943.0944 21.74463 22.36559 12.7954049
#> 85 8.4 942.4588 21.94332 22.57775 13.0201200
#> 86 8.5 941.8176 22.14362 22.79177 13.2469661
#> 87 8.6 941.1709 22.34552 23.00766 13.4759616
#> 88 8.7 940.5184 22.54905 23.22544 13.7071256
#> 89 8.8 939.8602 22.75420 23.44512 13.9404768
#> 90 8.9 939.1963 22.96099 23.66671 14.1760344
#> 91 9.0 938.5265 23.16943 23.89023 14.4138175
#> 92 9.1 937.8510 23.37951 24.11569 14.6538454
#> 93 9.2 937.1695 23.59126 24.34310 14.8961378
#> 94 9.3 936.4821 23.80468 24.57248 15.1407140
#> 95 9.4 935.7888 24.01978 24.80384 15.3875940
#> 96 9.5 935.0894 24.23656 25.03720 15.6367976
#> 97 9.6 934.3840 24.45504 25.27257 15.8883447
#> 98 9.7 933.6726 24.67522 25.50996 16.1422556
#> 99 9.8 932.9550 24.89711 25.74938 16.3985506
#> 100 9.9 932.2312 25.12072 25.99086 16.6572501
#> 101 10.0 931.5012 25.34606 26.23440 16.9183746
#> 102 10.1 930.7649 25.57312 26.48002 17.1819450
#> 103 10.2 930.0224 25.80193 26.72773 17.4479819
#> 104 10.3 929.2735 26.03249 26.97754 17.7165065
#> 105 10.4 928.5182 26.26481 27.22948 17.9875399
#> 106 10.5 927.7565 26.49889 27.48355 18.2611033
#> 107 10.6 926.9883 26.73474 27.73977 18.5372181
#> 108 10.7 926.2136 26.97237 27.99815 18.8159059
#> 109 10.8 925.4323 27.21178 28.25871 19.0971883
#> 110 10.9 924.6445 27.45299 28.52145 19.3810873
#> 111 11.0 923.8500 27.69600 28.78640 19.6676247
#> 112 11.1 923.0488 27.94081 29.05357 19.9568227
#> 113 11.2 922.2409 28.18744 29.32297 20.2487035
#> 114 11.3 921.4262 28.43588 29.59461 20.5432895
#> 115 11.4 920.6047 28.68616 29.86851 20.8406032
#> 116 11.5 919.7764 28.93827 30.14469 21.1406674
#> 117 11.6 918.9411 29.19221 30.42316 21.4435047
#> 118 11.7 918.0989 29.44801 30.70392 21.7491382
#> 119 11.8 917.2498 29.70565 30.98700 22.0575908
#> 120 11.9 916.3936 29.96515 31.27241 22.3688860
#> 121 12.0 915.5303 30.22651 31.56016 22.6830469
#> 122 12.1 914.6599 30.48975 31.85027 23.0000971
#> 123 12.2 913.7823 30.75486 32.14275 23.3200603
#> 124 12.3 912.8976 31.02184 32.43762 23.6429601
#> 125 12.4 912.0056 31.29072 32.73488 23.9688206
#> 126 12.5 911.1063 31.56148 33.03455 24.2976658
#> 127 12.6 910.1997 31.83414 33.33665 24.6295198
#> 128 12.7 909.2857 32.10870 33.64119 24.9644069
#> 129 12.8 908.3643 32.38516 33.94818 25.3023518
#> 130 12.9 907.4355 32.66353 34.25764 25.6433788
#> 131 13.0 906.4991 32.94382 34.56957 25.9875128
#> 132 13.1 905.5552 33.22602 34.88400 26.3347786
#> 133 13.2 904.6037 33.51014 35.20094 26.6852012
#> 134 13.3 903.6446 33.79619 35.52039 27.0388058
#> 135 13.4 902.6778 34.08416 35.84238 27.3956175
#> 136 13.5 901.7034 34.37407 36.16692 27.7556619
#> 137 13.6 900.7211 34.66591 36.49401 28.1189644
#> 138 13.7 899.7311 34.95969 36.82368 28.4855507
#> 139 13.8 898.7332 35.25541 37.15593 28.8554466
#> 140 13.9 897.7275 35.55307 37.49078 29.2286780
#> 141 14.0 896.7138 35.85268 37.82824 29.6052709
#> 142 14.1 895.6922 36.15423 38.16833 29.9852516
#> 143 14.2 894.6626 36.45773 38.51105 30.3686463
#> 144 14.3 893.6249 36.76319 38.85642 30.7554814
#> 145 14.4 892.5792 37.07059 39.20445 31.1457835
#> 146 14.5 891.5253 37.37995 39.55516 31.5395793
#> 147 14.6 890.4633 37.69126 39.90855 31.9368956
#> 148 14.7 889.3931 38.00452 40.26464 32.3377594
#> 149 14.8 888.3146 38.31974 40.62344 32.7421975
#> 150 14.9 887.2279 38.63692 40.98497 33.1502373
#> 151 15.0 886.1328 38.95605 41.34922 33.5619059
#> 152 15.1 885.0294 39.27713 41.71623 33.9772309
#> 153 15.2 883.9176 39.60017 42.08599 34.3962397
#> 154 15.3 882.7974 39.92515 42.45852 34.8189599
#> 155 15.4 881.6687 40.25209 42.83383 35.2454193
#> 156 15.5 880.5314 40.58098 43.21193 35.6756458
#> 157 15.6 879.3857 40.91182 43.59283 36.1096672
#> 158 15.7 878.2313 41.24461 43.97655 36.5475118
#> 159 15.8 877.0684 41.57933 44.36309 36.9892076
#> 160 15.9 875.8968 41.91600 44.75246 37.4347830
#> 161 16.0 874.7164 42.25460 45.14468 37.8842664
#> 162 16.1 873.5274 42.59514 45.53976 38.3376862
#> 163 16.2 872.3296 42.93761 45.93770 38.7950711
#> 164 16.3 871.1230 43.28200 46.33851 39.2564497
#> 165 16.4 869.9076 43.62832 46.74221 39.7218509
#> 166 16.5 868.6833 43.97655 47.14880 40.1913036
#> 167 16.6 867.4502 44.32670 47.55830 40.6648367
#> 168 16.7 866.2081 44.67875 47.97071 41.1424793
#> 169 16.8 864.9570 45.03270 48.38604 41.6242606
#> 170 16.9 863.6969 45.38855 48.80430 42.1102098
#> 171 17.0 862.4279 45.74629 49.22550 42.6003564
#> 172 17.1 861.1497 46.10590 49.64964 43.0947296
#> 173 17.2 859.8625 46.46740 50.07674 43.5933591
#> 174 17.3 858.5662 46.83075 50.50681 44.0962743
#> 175 17.4 857.2607 47.19597 50.93984 44.6035051
#> 176 17.5 855.9460 47.56304 51.37585 45.1150811
#> 177 17.6 854.6222 47.93194 51.81485 45.6310321
#> 178 17.7 853.2891 48.30268 52.25683 46.1513880
#> 179 17.8 851.9468 48.67524 52.70182 46.6761787
#> 180 17.9 850.5951 49.04962 53.14981 47.2054344
#> 181 18.0 849.2342 49.42579 53.60081 47.7391850
#> 182 18.1 847.8640 49.80376 54.05483 48.2774606
#> 183 18.2 846.4843 50.18351 54.51187 48.8202916
#> 184 18.3 845.0953 50.56502 54.97193 49.3677080
#> 185 18.4 843.6969 50.94829 55.43503 49.9197403
#> 186 18.5 842.2891 51.33331 55.90116 50.4764187
#> 187 18.6 840.8718 51.72005 56.37034 51.0377737
#> 188 18.7 839.4451 52.10852 56.84256 51.6038357
#> 189 18.8 838.0089 52.49868 57.31783 52.1746351
#> 190 18.9 836.5631 52.89053 57.79615 52.7502024
#> 191 19.0 835.1078 53.28406 58.27753 53.3305683
#> 192 19.1 833.6430 53.67925 58.76196 53.9157632
#> 193 19.2 832.1686 54.07608 59.24946 54.5058178
#> 194 19.3 830.6847 54.47453 59.74002 55.1007627
#> 195 19.4 829.1911 54.87460 60.23364 55.7006284
#> 196 19.5 827.6880 55.27625 60.73033 56.3054457
#> 197 19.6 826.1752 55.67949 61.23009 56.9152452
#> 198 19.7 824.6528 56.08428 61.73291 57.5300577
#> 199 19.8 823.1207 56.49060 62.23880 58.1499136
#> 200 19.9 821.5790 56.89845 62.74776 58.7748439
#> 201 20.0 820.0275 57.30779 63.25978 59.4048790
#> 202 20.1 818.4665 57.71861 63.77487 60.0400497
#> 203 20.2 816.8957 58.13090 64.29303 60.6803867
#> 204 20.3 815.3152 58.54461 64.81425 61.3259205
#> 205 20.4 813.7250 58.95975 65.33853 61.9766818
#> 206 20.5 812.1252 59.37627 65.86587 62.6327012
#> 207 20.6 810.5156 59.79417 66.39626 63.2940093
#> 208 20.7 808.8962 60.21341 66.92971 63.9606366
#> 209 20.8 807.2672 60.63397 67.46620 64.6326136
#> 210 20.9 805.6285 61.05584 68.00574 65.3099707
#> 211 21.0 803.9800 61.47897 68.54832 65.9927385
#> 212 21.1 802.3218 61.90336 69.09393 66.6809472
#> 213 21.2 800.6538 62.32896 69.64257 67.3746272
#> 214 21.3 798.9762 62.75577 70.19424 68.0738087
#> 215 21.4 797.2888 63.18374 70.74891 68.7785219
#> 216 21.5 795.5918 63.61285 71.30660 69.4887970
#> 217 21.6 793.8850 64.04307 71.86729 70.2046640
#> 218 21.7 792.1685 64.47438 72.43098 70.9261529
#> 219 21.8 790.4423 64.90674 72.99765 71.6532935
#> 220 21.9 788.7065 65.34012 73.56729 72.3861157
#> 221 22.0 786.9609 65.77450 74.13990 73.1246492
#> 222 22.1 785.2058 66.20984 74.71547 73.8689236
#> 223 22.2 783.4409 66.64612 75.29398 74.6189685
#> 224 22.3 781.6665 67.08329 75.87543 75.3748131
#> 225 22.4 779.8824 67.52133 76.45980 76.1364868
#> 226 22.5 778.0887 67.96021 77.04708 76.9040188
#> 227 22.6 776.2854 68.39988 77.63726 77.6774382
#> 228 22.7 774.4726 68.84032 78.23033 78.4567738
#> 229 22.8 772.6502 69.28149 78.82627 79.2420543
#> 230 22.9 770.8183 69.72336 79.42506 80.0333086
#> 231 23.0 768.9769 70.16588 80.02669 80.8305650
#> 232 23.1 767.1260 70.60903 80.63116 81.6338519
#> 233 23.2 765.2656 71.05276 81.23843 82.4431975
#> 234 23.3 763.3958 71.49704 81.84849 83.2586297
#> 235 23.4 761.5167 71.94184 82.46133 84.0801766
#> 236 23.5 759.6281 72.38710 83.07693 84.9078656
#> 237 23.6 757.7302 72.83279 83.69527 85.7417243
#> 238 23.7 755.8230 73.27888 84.31633 86.5817801
#> 239 23.8 753.9065 73.72532 84.94009 87.4280600
#> 240 23.9 751.9808 74.17207 85.56654 88.2805909
#> 241 24.0 750.0459 74.61909 86.19564 89.1393996
#> 242 24.1 748.1018 75.06633 86.82738 90.0045125
#> 243 24.2 746.1485 75.51376 87.46174 90.8759559
#> 244 24.3 744.1862 75.96133 88.09869 91.7537559
#> 245 24.4 742.2149 76.40900 88.73821 92.6379382
#> 246 24.5 740.2345 76.85673 89.38028 93.5285285
#> 247 24.6 738.2451 77.30446 90.02486 94.4255521
#> 248 24.7 736.2469 77.75216 90.67195 95.3290341
#> 249 24.8 734.2397 78.19977 91.32150 96.2389993
#> 250 24.9 732.2238 78.64726 91.97350 97.1554723
#> 251 25.0 730.1990 79.09458 92.62791 98.0784774
#> 252 25.1 728.1656 79.54167 93.28472 99.0080385
#> 253 25.2 726.1234 79.98850 93.94388 99.9441795
#> 254 25.3 724.0727 80.43501 94.60537 100.8869238
#> 255 25.4 722.0134 80.88115 95.26916 101.8362946
#> 256 25.5 719.9456 81.32688 95.93522 102.7923146
#> 257 25.6 717.8693 81.77215 96.60352 103.7550064
#> 258 25.7 715.7847 82.21690 97.27403 104.7243923
#> 259 25.8 713.6917 82.66109 97.94670 105.7004942
#> 260 25.9 711.5905 83.10467 98.62152 106.6833336
#> 261 26.0 709.4810 83.54758 99.29845 107.6729317
#> 262 26.1 707.3635 83.98977 99.97745 108.6693095
#> 263 26.2 705.2378 84.43119 100.65848 109.6724874
#> 264 26.3 703.1042 84.87179 101.34151 110.6824857
#> 265 26.4 700.9626 85.31152 102.02651 111.6993242
#> 266 26.5 698.8132 85.75032 102.71343 112.7230223
#> 267 26.6 696.6560 86.18814 103.40224 113.7535991
#> 268 26.7 694.4911 86.62493 104.09290 114.7910732
#> 269 26.8 692.3186 87.06062 104.78537 115.8354631
#> 270 26.9 690.1384 87.49517 105.47960 116.8867865
#> 271 27.0 687.9508 87.92853 106.17557 117.9450609
#> 272 27.1 685.7559 88.36063 106.87322 119.0103034
#> 273 27.2 683.5535 88.79142 107.57251 120.0825307
#> 274 27.3 681.3440 89.22085 108.27341 121.1617590
#> 275 27.4 679.1273 89.64885 108.97586 122.2480041
#> 276 27.5 676.9035 90.07538 109.67983 123.3412813
#> 277 27.6 674.6727 90.50038 110.38527 124.4416056
#> 278 27.7 672.4351 90.92378 111.09213 125.5489914
#> 279 27.8 670.1906 91.34554 111.80036 126.6634527
#> 280 27.9 667.9395 91.76560 112.50993 127.7850031
#> 281 28.0 665.6817 92.18389 113.22077 128.9136555
#> 282 28.1 663.4174 92.60036 113.93285 130.0494226
#> 283 28.2 661.1466 93.01496 114.64611 131.1923164
#> 284 28.3 658.8695 93.42762 115.36051 132.3423486
#> 285 28.4 656.5862 93.83828 116.07599 133.4995302
#> 286 28.5 654.2967 94.24690 116.79250 134.6638718
#> 287 28.6 652.0012 94.65341 117.51000 135.8353835
#> 288 28.7 649.6998 95.05774 118.22842 137.0140749
#> 289 28.8 647.3925 95.45986 118.94772 138.1999549
#> 290 28.9 645.0794 95.85968 119.66784 139.3930321
#> 291 29.0 642.7608 96.25716 120.38873 140.5933143
#> 292 29.1 640.4366 96.65225 121.11034 141.8008091
#> 293 29.2 638.1070 97.04487 121.83260 143.0155233
#> 294 29.3 635.7721 97.43497 122.55546 144.2374631
#> 295 29.4 633.4320 97.82249 123.27887 145.4666343
#> 296 29.5 631.0868 98.20737 124.00276 146.7030421
#> 297 29.6 628.7367 98.58956 124.72709 147.9466910
#> 298 29.7 626.3816 98.96900 125.45178 149.1975851
#> 299 29.8 624.0219 99.34563 126.17679 150.4557277
#> 300 29.9 621.6574 99.71938 126.90205 151.7211218
#> 301 30.0 619.2885 100.09021 127.62751 152.9937695
#> 302 30.1 616.9152 100.45805 128.35309 154.2736724
#> 303 30.2 614.5376 100.82284 129.07875 155.5608315
#> 304 30.3 612.1558 101.18454 129.80441 156.8552473
#> 305 30.4 609.7700 101.54308 130.53002 158.1569195
#> 306 30.5 607.3802 101.89839 131.25551 159.4658473
#> 307 30.6 604.9867 102.25044 131.98082 160.7820292
#> 308 30.7 602.5895 102.59916 132.70589 162.1054630
#> 309 30.8 600.1887 102.94449 133.43065 163.4361460
#> 310 30.9 597.7845 103.28637 134.15504 164.7740748
#> 311 31.0 595.3770 103.62476 134.87898 166.1192452
#> 312 31.1 592.9663 103.95960 135.60242 167.4716527
#> 313 31.2 590.5526 104.29082 136.32530 168.8312918
#> 314 31.3 588.1359 104.61838 137.04753 170.1981565
#> 315 31.4 585.7165 104.94222 137.76906 171.5722401
#> 316 31.5 583.2944 105.26229 138.48981 172.9535351
#> 317 31.6 580.8697 105.57853 139.20973 174.3420336
#> 318 31.7 578.4426 105.89089 139.92874 175.7377267
#> 319 31.8 576.0133 106.19932 140.64677 177.1406051
#> 320 31.9 573.5818 106.50377 141.36375 178.5506586
#> 321 32.0 571.1483 106.80418 142.07962 179.9678764
#> 322 32.1 568.7130 107.10050 142.79430 181.3922471
#> 323 32.2 566.2758 107.39268 143.50773 182.8237583
#> 324 32.3 563.8371 107.68067 144.21983 184.2623973
#> 325 32.4 561.3969 107.96442 144.93054 185.7081503
#> 326 32.5 558.9553 108.24389 145.63978 187.1610031
#> 327 32.6 556.5126 108.51902 146.34747 188.6209407
#> 328 32.7 554.0687 108.78977 147.05356 190.0879473
#> 329 32.8 551.6239 109.05608 147.75797 191.5620064
#> 330 32.9 549.1784 109.31792 148.46062 193.0431008
#> 331 33.0 546.7321 109.57523 149.16145 194.5312127
#> 332 33.1 544.2853 109.82797 149.86038 196.0263235
#> 333 33.2 541.8381 110.07610 150.55734 197.5284137
#> 334 33.3 539.3907 110.31958 151.25225 199.0374634
#> 335 33.4 536.9431 110.55835 151.94505 200.5534517
#> 336 33.5 534.4956 110.79238 152.63566 202.0763571
#> 337 33.6 532.0482 111.02163 153.32401 203.6061574
#> 338 33.7 529.6011 111.24605 154.01002 205.1428295
#> 339 33.8 527.1544 111.46560 154.69363 206.6863498
#> 340 33.9 524.7083 111.68026 155.37475 208.2366938
#> 341 34.0 522.2629 111.88997 156.05332 209.7938362
#> 342 34.1 519.8183 112.09470 156.72926 211.3577513
#> 343 34.2 517.3747 112.29441 157.40249 212.9284124
#> 344 34.3 514.9322 112.48907 158.07296 214.5057920
#> 345 34.4 512.4909 112.67865 158.74057 216.0898620
#> 346 34.5 510.0510 112.86310 159.40527 217.6805937
#> 347 34.6 507.6127 113.04240 160.06697 219.2779574
#> 348 34.7 505.1760 113.21652 160.72560 220.8819229
#> 349 34.8 502.7410 113.38541 161.38109 222.4924590
#> 350 34.9 500.3080 113.54906 162.03337 224.1095340
#> 351 35.0 497.8771 113.70744 162.68236 225.7331155
#> 352 35.1 495.4483 113.86051 163.32800 227.3631701
#> 353 35.2 493.0219 114.00824 163.97020 228.9996640
#> 354 35.3 490.5979 114.15062 164.60890 230.6425624
#> 355 35.4 488.1765 114.28762 165.24402 232.2918300
#> 356 35.5 485.7579 114.41920 165.87550 233.9474307
#> 357 35.6 483.3421 114.54536 166.50326 235.6093276
#> 358 35.7 480.9292 114.66606 167.12723 237.2774832
#> 359 35.8 478.5195 114.78129 167.74733 238.9518593
#> 360 35.9 476.1130 114.89103 168.36351 240.6324168
#> 361 36.0 473.7100 114.99525 168.97568 242.3191161
#> 362 36.1 471.3104 115.09394 169.58378 244.0119168
#> 363 36.2 468.9144 115.18708 170.18774 245.7107778
#> 364 36.3 466.5222 115.27466 170.78749 247.4156575
#> 365 36.4 464.1339 115.35666 171.38295 249.1265133
#> 366 36.5 461.7496 115.43307 171.97407 250.8433020
#> 367 36.6 459.3694 115.50387 172.56077 252.5659800
#> 368 36.7 456.9935 115.56906 173.14299 254.2945025
#> 369 36.8 454.6219 115.62862 173.72065 256.0288245
#> 370 36.9 452.2549 115.68254 174.29370 257.7689001
#> 371 37.0 449.8924 115.73082 174.86206 259.5146828
#> 372 37.1 447.5348 115.77345 175.42567 261.2661254
#> 373 37.2 445.1819 115.81043 175.98446 263.0231801
#> 374 37.3 442.8341 115.84174 176.53837 264.7857984
#> 375 37.4 440.4913 115.86739 177.08734 266.5539311
#> 376 37.5 438.1538 115.88737 177.63130 268.3275285
#> 377 37.6 435.8216 115.90169 178.17019 270.1065402
#> 378 37.7 433.4948 115.91033 178.70394 271.8909152
#> 379 37.8 431.1736 115.91331 179.23250 273.6806017
#> 380 37.9 428.8580 115.91062 179.75581 275.4755477
#> 381 38.0 426.5482 115.90227 180.27379 277.2757001
#> 382 38.1 424.2443 115.88826 180.78640 279.0810056
#> 383 38.2 421.9464 115.86859 181.29357 280.8914100
#> 384 38.3 419.6546 115.84329 181.79525 282.7068588
#> 385 38.4 417.3690 115.81234 182.29138 284.5272966
#> 386 38.5 415.0897 115.77576 182.78190 286.3526677
#> 387 38.6 412.8168 115.73356 183.26676 288.1829157
#> 388 38.7 410.5504 115.68576 183.74589 290.0179837
#> 389 38.8 408.2906 115.63236 184.21925 291.8578143
#> 390 38.9 406.0375 115.57337 184.68678 293.7023493
#> 391 39.0 403.7912 115.50881 185.14843 295.5515303
#> 392 39.1 401.5519 115.43870 185.60415 297.4052981
#> 393 39.2 399.3195 115.36305 186.05388 299.2635933
#> 394 39.3 397.0942 115.28188 186.49758 301.1263556
#> 395 39.4 394.8761 115.19521 186.93519 302.9935245
#> 396 39.5 392.6652 115.10305 187.36666 304.8650389
#> 397 39.6 390.4618 115.00543 187.79196 306.7408372
#> 398 39.7 388.2657 114.90238 188.21103 308.6208573
#> 399 39.8 386.0772 114.79390 188.62382 310.5050368
#> 400 39.9 383.8964 114.68003 189.03029 312.3933126
#> 401 40.0 381.7232 114.56079 189.43040 314.2856214
#> 402 40.1 379.5578 114.43621 189.82410 316.1818993
#> 403 40.2 377.4003 114.30630 190.21135 318.0820819
#> 404 40.3 375.2507 114.17111 190.59211 319.9861047
#> 405 40.4 373.1091 114.03066 190.96634 321.8939024
#> 406 40.5 370.9756 113.88497 191.33400 323.8054096
#> 407 40.6 368.8503 113.73408 191.69505 325.7205603
#> 408 40.7 366.7332 113.57803 192.04945 327.6392884
#> 409 40.8 364.6245 113.41683 192.39717 329.5615270
#> 410 40.9 362.5241 113.25053 192.73817 331.4872093
#> 411 41.0 360.4322 113.07915 193.07241 333.4162679
#> 412 41.1 358.3487 112.90274 193.39987 335.3486350
#> 413 41.2 356.2739 112.72133 193.72052 337.2842426
#> 414 41.3 354.2077 112.53496 194.03431 339.2230225
#> 415 41.4 352.1502 112.34365 194.34122 341.1649058
#> 416 41.5 350.1015 112.14746 194.64122 343.1098238
#> 417 41.6 348.0616 111.94642 194.93428 345.0577071
#> 418 41.7 346.0306 111.74057 195.22038 347.0084862
#> 419 41.8 344.0085 111.52994 195.49949 348.9620914
#> 420 41.9 341.9954 111.31459 195.77158 350.9184526
#> 421 42.0 339.9913 111.09455 196.03663 352.8774996
#> 422 42.1 337.9963 110.86987 196.29462 354.8391617
#> 423 42.2 336.0105 110.64058 196.54553 356.8033684
#> 424 42.3 334.0339 110.40674 196.78933 358.7700486
#> 425 42.4 332.0665 110.16839 197.02601 360.7391312
#> 426 42.5 330.1084 109.92557 197.25554 362.7105449
#> 427 42.6 328.1595 109.67832 197.47791 364.6842181
#> 428 42.7 326.2201 109.42670 197.69311 366.6600792
#> 429 42.8 324.2901 109.17076 197.90111 368.6380563
#> 430 42.9 322.3695 108.91053 198.10191 370.6180775
#> 431 43.0 320.4584 108.64607 198.29549 372.6000705
#> 432 43.1 318.5568 108.37743 198.48184 374.5839632
#> 433 43.2 316.6647 108.10466 198.66095 376.5696832
#> 434 43.3 314.7822 107.82780 198.83281 378.5571580
#> 435 43.4 312.9094 107.54690 198.99740 380.5463151
#> 436 43.5 311.0462 107.26203 199.15473 382.5370818
#> 437 43.6 309.1926 106.97322 199.30479 384.5293855
#> 438 43.7 307.3488 106.68053 199.44756 386.5231533
#> 439 43.8 305.5146 106.38401 199.58305 388.5183124
#> 440 43.9 303.6902 106.08372 199.71126 390.5147901
#> 441 44.0 301.8756 105.77970 199.83218 392.5125133
#> 442 44.1 300.0708 105.47202 199.94581 394.5114093
#> 443 44.2 298.2757 105.16071 200.05214 396.5114051
#> 444 44.3 296.4905 104.84585 200.15119 398.5124279
#> 445 44.4 294.7152 104.52747 200.24295 400.5144047
#> 446 44.5 292.9497 104.20565 200.32743 402.5172627
#> 447 44.6 291.1940 103.88042 200.40463 404.5209291
#> 448 44.7 289.4483 103.55184 200.47456 406.5253311
#> 449 44.8 287.7124 103.21998 200.53722 408.5303960
#> 450 44.9 285.9864 102.88489 200.59262 410.5360512
#> 451 45.0 284.2704 102.54661 200.64076 412.5422242
#> 452 45.1 282.5643 102.20521 200.68167 414.5488424
#> 453 45.2 280.8681 101.86075 200.71534 416.5558334
#> 454 45.3 279.1818 101.51328 200.74180 418.5631251
#> 455 45.4 277.5055 101.16285 200.76104 420.5706453
#> 456 45.5 275.8391 100.80952 200.77309 422.5783220
#> 457 45.6 274.1826 100.45335 200.77797 424.5860833
#> 458 45.7 272.5361 100.09439 200.77567 426.5938574
#> 459 45.8 270.8995 99.73271 200.76623 428.6015729
#> 460 45.9 269.2728 99.36835 200.74966 430.6091583
#> 461 46.0 267.6561 99.00138 200.72598 432.6165425
#> 462 46.1 266.0493 98.63185 200.69521 434.6236543
#> 463 46.2 264.4524 98.25981 200.65736 436.6304230
#> 464 46.3 262.8654 97.88533 200.61246 438.6367779
#> 465 46.4 261.2884 97.50846 200.56053 440.6426487
#> 466 46.5 259.7212 97.12926 200.50159 442.6479651
#> 467 46.6 258.1639 96.74778 200.43568 444.6526573
#> 468 46.7 256.6165 96.36408 200.36280 446.6566554
#> 469 46.8 255.0789 95.97822 200.28299 448.6598902
#> 470 46.9 253.5512 95.59025 200.19628 450.6622923
#> 471 47.0 252.0333 95.20023 200.10269 452.6637928
#> 472 47.1 250.5252 94.80821 200.00224 454.6643231
#> 473 47.2 249.0270 94.41426 199.89498 456.6638149
#> 474 47.3 247.5385 94.01841 199.78092 458.6622000
#> 475 47.4 246.0597 93.62075 199.66011 460.6594108
#> 476 47.5 244.5908 93.22130 199.53256 462.6553798
#> 477 47.6 243.1315 92.82014 199.39832 464.6500397
#> 478 47.7 241.6819 92.41732 199.25741 466.6433239
#> 479 47.8 240.2421 92.01288 199.10987 468.6351659
#> 480 47.9 238.8119 91.60689 198.95574 470.6254994
#> 481 48.0 237.3913 91.19940 198.79505 472.6142588
#> 482 48.1 235.9803 90.79047 198.62783 474.6013786
#> 483 48.2 234.5789 90.38014 198.45412 476.5867938
#> 484 48.3 233.1871 89.96847 198.27396 478.5704395
#> 485 48.4 231.8048 89.55551 198.08739 480.5522517
#> 486 48.5 230.4321 89.14132 197.89445 482.5321662
#> 487 48.6 229.0688 88.72595 197.69517 484.5101195
#> 488 48.7 227.7149 88.30945 197.48960 486.4860486
#> 489 48.8 226.3705 87.89187 197.27777 488.4598907
#> 490 48.9 225.0354 87.47326 197.05973 490.4315833
#> 491 49.0 223.7097 87.05368 196.83552 492.4010647
#> 492 49.1 222.3934 86.63317 196.60518 494.3682733
#> 493 49.2 221.0863 86.21179 196.36876 496.3331481
#> 494 49.3 219.7885 85.78959 196.12629 498.2956283
#> 495 49.4 218.4999 85.36660 195.87783 500.2556539
#> 496 49.5 217.2205 84.94290 195.62342 502.2131651
#> 497 49.6 215.9503 84.51851 195.36309 504.1681026
#> 498 49.7 214.6892 84.09349 195.09691 506.1204074
#> 499 49.8 213.4372 83.66790 194.82491 508.0700214
#> 500 49.9 212.1942 83.24177 194.54714 510.0168864
#> 501 50.0 210.9603 82.81515 194.26365 511.9609452
# Open population with births and deaths
model_seir(
init = c(S = 980, E = 10, I = 10),
params = c(beta = 0.3, alpha = 0.2, gamma = 0.1, b = 0.01, d = 0.01),
times = seq(0, 200, by = 1)
)
#> time S E I R
#> 1 0 980.0000 10.00000 10.00000 0.000000
#> 2 1 977.1428 10.88028 10.93588 1.041048
#> 3 2 974.0397 11.84277 11.94887 2.168637
#> 4 3 970.6724 12.89081 13.04682 3.389968
#> 5 4 967.0209 14.02867 14.23748 4.712952
#> 6 5 963.0639 15.26124 15.52867 6.146189
#> 7 6 958.7788 16.59384 16.92836 7.698981
#> 8 7 954.1419 18.03206 18.44473 9.381340
#> 9 8 949.1282 19.58163 20.08618 11.204003
#> 10 9 943.7119 21.24829 21.86132 13.178447
#> 11 10 937.8665 23.03765 23.77895 15.316902
#> 12 11 931.5646 24.95508 25.84799 17.632357
#> 13 12 924.7785 27.00552 28.07741 20.138563
#> 14 13 917.4805 29.19333 30.47611 22.850026
#> 15 14 909.6430 31.52211 33.05286 25.781985
#> 16 15 901.2390 33.99451 35.81606 28.950384
#> 17 16 892.2425 36.61198 38.77367 32.371826
#> 18 17 882.6290 39.37454 41.93293 36.063504
#> 19 18 872.3761 42.28055 45.30018 40.043116
#> 20 19 861.4642 45.32645 48.88062 44.328764
#> 21 20 849.8767 48.50648 52.67801 48.938815
#> 22 21 837.6014 51.81246 56.69442 53.891750
#> 23 22 824.6306 55.23356 60.92987 59.205962
#> 24 23 810.9623 58.75609 65.38208 64.899559
#> 25 24 796.6004 62.36337 70.04612 70.990114
#> 26 25 781.5559 66.03563 74.91413 77.494391
#> 27 26 765.8470 69.75002 79.97500 84.428036
#> 28 27 749.4999 73.48068 85.21418 91.805288
#> 29 28 732.5490 77.19894 90.61346 99.638591
#> 30 29 715.0373 80.87364 96.15084 107.938265
#> 31 30 697.0158 84.47150 101.80050 116.712159
#> 32 31 678.5441 87.95776 107.53286 125.965284
#> 33 32 659.6890 91.29676 113.31474 135.699476
#> 34 33 640.5245 94.45276 119.10964 145.913083
#> 35 34 621.1304 97.39073 124.87815 156.600687
#> 36 35 601.5914 100.07725 130.57847 167.752882
#> 37 36 581.9954 102.48142 136.16706 179.356100
#> 38 37 562.4325 104.57568 141.59935 191.392520
#> 39 38 542.9927 106.33664 146.83061 203.840050
#> 40 39 523.7651 107.74573 151.81679 216.672391
#> 41 40 504.8356 108.78976 156.51541 229.859194
#> 42 41 486.2860 109.46125 160.88646 243.366302
#> 43 42 468.1921 109.75859 164.89328 257.156076
#> 44 43 450.6229 109.68605 168.50326 271.187800
#> 45 44 433.6398 109.25349 171.68854 285.418150
#> 46 45 417.2957 108.47601 174.42657 299.801721
#> 47 46 401.6347 107.37332 176.70043 314.291597
#> 48 47 386.6919 105.96910 178.49911 328.839935
#> 49 48 372.4937 104.29019 179.81755 343.398572
#> 50 49 359.0580 102.36581 180.65654 357.919611
#> 51 50 346.3949 100.22668 181.02247 372.355994
#> 52 51 334.5067 97.90428 180.92697 386.662031
#> 53 52 323.3896 95.43007 180.38645 400.793887
#> 54 53 313.0337 92.83480 179.42148 414.710008
#> 55 54 303.4243 90.14802 178.05623 428.371483
#> 56 55 294.5424 87.39753 176.31776 441.742346
#> 57 56 286.3657 84.60910 174.23542 454.789800
#> 58 57 278.8693 81.80615 171.84013 467.484376
#> 59 58 272.0265 79.00965 169.16380 479.800030
#> 60 59 265.8090 76.23804 166.23874 491.714180
#> 61 60 260.1879 73.50722 163.09716 503.207678
#> 62 61 255.1339 70.83064 159.77066 514.264748
#> 63 62 250.6178 68.21943 156.28989 524.872870
#> 64 63 246.6106 65.68254 152.68420 535.022634
#> 65 64 243.0842 63.22690 148.98137 544.707569
#> 66 65 240.0109 60.85768 145.20743 553.923949
#> 67 66 237.3645 58.57844 141.38653 562.670579
#> 68 67 235.1193 56.39133 137.54082 570.948581
#> 69 68 233.2511 54.29732 133.69046 578.761170
#> 70 69 231.7367 52.29635 129.85356 586.113434
#> 71 70 230.5541 50.38752 126.04627 593.012113
#> 72 71 229.6825 48.56925 122.28282 599.465395
#> 73 72 229.1023 46.83938 118.57558 605.482699
#> 74 73 228.7949 45.19536 114.93522 611.074501
#> 75 74 228.7428 43.63429 111.37073 616.252155
#> 76 75 228.9296 42.15305 107.88964 621.027718
#> 77 76 229.3398 40.74838 104.49806 625.413804
#> 78 77 229.9588 39.41694 101.20085 629.423448
#> 79 78 230.7729 38.15536 98.00172 633.069979
#> 80 79 231.7695 36.96027 94.90336 636.366912
#> 81 80 232.9362 35.82838 91.90754 639.327847
#> 82 81 234.2619 34.75645 89.01525 641.966386
#> 83 82 235.7358 33.74137 86.22675 644.296059
#> 84 83 237.3479 32.78013 83.54171 646.330251
#> 85 84 239.0887 31.86985 80.95926 648.082158
#> 86 85 240.9494 31.00777 78.47811 649.564735
#> 87 86 242.9215 30.19129 76.09657 650.790662
#> 88 87 244.9971 29.41792 73.81267 651.772306
#> 89 88 247.1688 28.68534 71.62417 652.521705
#> 90 89 249.4295 27.99132 69.52865 653.050541
#> 91 90 251.7725 27.33381 67.52352 653.370134
#> 92 91 254.1917 26.71084 65.60609 653.491427
#> 93 92 256.6809 26.12058 63.77358 653.424980
#> 94 93 259.2345 25.56131 62.02318 653.180972
#> 95 94 261.8473 25.03144 60.35206 652.769199
#> 96 95 264.5141 24.52944 58.75736 652.199075
#> 97 96 267.2302 24.05391 57.23628 651.479641
#> 98 97 269.9909 23.60353 55.78602 650.619568
#> 99 98 272.7919 23.17706 54.40386 649.627165
#> 100 99 275.6291 22.77335 53.08712 648.510392
#> 101 100 278.4986 22.39132 51.83318 647.276864
#> 102 101 281.3967 22.02995 50.63951 645.933864
#> 103 102 284.3197 21.68831 49.50366 644.488358
#> 104 103 287.2643 21.36550 48.42325 642.946998
#> 105 104 290.2272 21.06069 47.39600 641.316139
#> 106 105 293.2053 20.77312 46.41969 639.601851
#> 107 106 296.1958 20.50205 45.49222 637.809927
#> 108 107 299.1957 20.24680 44.61156 635.945898
#> 109 108 302.2025 20.00674 43.77577 634.015040
#> 110 109 305.2134 19.78126 42.98298 632.022391
#> 111 110 308.2260 19.56982 42.23144 629.972754
#> 112 111 311.2380 19.37187 41.51944 627.870717
#> 113 112 314.2470 19.18693 40.84538 625.720654
#> 114 113 317.2510 19.01453 40.20773 623.526741
#> 115 114 320.2478 18.85425 39.60502 621.292963
#> 116 115 323.2353 18.70567 39.03588 619.023125
#> 117 116 326.2118 18.56841 38.49897 616.720859
#> 118 117 329.1752 18.44211 37.99306 614.389632
#> 119 118 332.1238 18.32644 37.51696 612.032757
#> 120 119 335.0560 18.22107 37.06954 609.653399
#> 121 120 337.9700 18.12571 36.64974 607.254582
#> 122 121 340.8642 18.04009 36.25656 604.839198
#> 123 122 343.7370 17.96393 35.88903 602.410011
#> 124 123 346.5871 17.89699 35.54625 599.969665
#> 125 124 349.4129 17.83904 35.22737 597.520693
#> 126 125 352.2130 17.78986 34.93158 595.065519
#> 127 126 354.9862 17.74925 34.65812 592.606456
#> 128 127 357.7310 17.71701 34.40626 590.145734
#> 129 128 360.4462 17.69296 34.17533 587.685483
#> 130 129 363.1307 17.67693 33.96467 585.227747
#> 131 130 365.7831 17.66876 33.77368 582.774496
#> 132 131 368.4023 17.66830 33.60178 580.327609
#> 133 132 370.9873 17.67541 33.44843 577.888893
#> 134 133 373.5368 17.68995 33.31312 575.460086
#> 135 134 376.0500 17.71180 33.19537 573.042862
#> 136 135 378.5256 17.74083 33.09471 570.638829
#> 137 136 380.9628 17.77693 33.01072 568.249534
#> 138 137 383.3605 17.82000 32.94299 565.876471
#> 139 138 385.7179 17.86993 32.89114 563.521074
#> 140 139 388.0339 17.92662 32.85480 561.184731
#> 141 140 390.3076 17.98998 32.83362 558.868776
#> 142 141 392.5383 18.05992 32.82729 556.574501
#> 143 142 394.7250 18.13636 32.83549 554.303152
#> 144 143 396.8669 18.21922 32.85793 552.055930
#> 145 144 398.9633 18.30840 32.89434 549.834000
#> 146 145 401.0132 18.40384 32.94445 547.638486
#> 147 146 403.0160 18.50546 33.00801 545.470477
#> 148 147 404.9710 18.61318 33.08479 543.331025
#> 149 148 406.8774 18.72693 33.17456 541.221149
#> 150 149 408.7344 18.84663 33.27709 539.141837
#> 151 150 410.5416 18.97221 33.39218 537.094044
#> 152 151 412.2981 19.10360 33.51963 535.078696
#> 153 152 414.0033 19.24072 33.65924 533.096691
#> 154 153 415.6568 19.38350 33.81082 531.148896
#> 155 154 417.2578 19.53185 33.97420 529.236154
#> 156 155 418.8058 19.68569 34.14918 527.359279
#> 157 156 420.3004 19.84495 34.33560 525.519063
#> 158 157 421.7409 20.00954 34.53327 523.716268
#> 159 158 423.1270 20.17937 34.74204 521.951634
#> 160 159 424.4581 20.35435 34.96172 520.225877
#> 161 160 425.7338 20.53438 35.19214 518.539686
#> 162 161 426.9538 20.71937 35.43314 516.893730
#> 163 162 428.1176 20.90920 35.68454 515.288650
#> 164 163 429.2250 21.10377 35.94616 513.725067
#> 165 164 430.2756 21.30297 36.21783 512.203576
#> 166 165 431.2692 21.50667 36.49937 510.724749
#> 167 166 432.2055 21.71476 36.79058 509.289133
#> 168 167 433.0844 21.92709 37.09128 507.897252
#> 169 168 433.9056 22.14353 37.40127 506.549606
#> 170 169 434.6691 22.36393 37.72034 505.246667
#> 171 170 435.3747 22.58814 38.04829 503.988886
#> 172 171 436.0224 22.81601 38.38490 502.776684
#> 173 172 436.6122 23.04737 38.72994 501.610459
#> 174 173 437.1442 23.28204 39.08318 500.490582
#> 175 174 437.6184 23.51984 39.44437 499.417393
#> 176 175 438.0349 23.76059 39.81327 498.391209
#> 177 176 438.3940 24.00409 40.18960 497.412313
#> 178 177 438.6958 24.25013 40.57310 496.480963
#> 179 178 438.9406 24.49851 40.96348 495.597383
#> 180 179 439.1288 24.74900 41.36044 494.761770
#> 181 180 439.2607 25.00139 41.76368 493.974284
#> 182 181 439.3366 25.25543 42.17287 493.235057
#> 183 182 439.3572 25.51088 42.58770 492.544186
#> 184 183 439.3230 25.76750 43.00782 491.901729
#> 185 184 439.2344 26.02504 43.43286 491.307715
#> 186 185 439.0922 26.28322 43.86248 490.762135
#> 187 186 438.8970 26.54179 44.29628 490.264941
#> 188 187 438.6496 26.80048 44.73388 489.816054
#> 189 188 438.3508 27.05900 45.17488 489.415349
#> 190 189 438.0014 27.31707 45.61887 489.062664
#> 191 190 437.6024 27.57441 46.06541 488.757796
#> 192 191 437.1547 27.83072 46.51409 488.500503
#> 193 192 436.6593 28.08572 46.96445 488.290502
#> 194 193 436.1174 28.33910 47.41605 488.127468
#> 195 194 435.5300 28.59057 47.86841 488.011033
#> 196 195 434.8983 28.83984 48.32107 487.940785
#> 197 196 434.2236 29.08659 48.77355 487.916272
#> 198 197 433.5071 29.33054 49.22536 487.936997
#> 199 198 432.7502 29.57139 49.67602 488.002418
#> 200 199 431.9542 29.80885 50.12503 488.111951
#> 201 200 431.1205 30.04261 50.57189 488.264968