Simulates the trajectory of the serosolver antibody model using specified parameters and optionally a specified antigenic map and infection history.
simulate_antibody_model(
pars,
times = NULL,
infection_history = NULL,
antigenic_map = NULL,
exponential_waning = FALSE
)either the original `par_tab` object (a data frame), or the vector of named model parameters, including `boost_long`, `boost_short`,`boost_delay`,`wane_long`,`wane_short`,`cr_long`, and `cr_short`.
the vector of time points at which to solve the model. Can be left to NULL if these times are included in `antigenic_map`.
the vector of infection times, each of which must be present in `times`. If NULL, an infection is simulated at the first value of `times`.
the antigenic map to solve the model with. Can be left to NULL to assume all biomarker IDs have the same antigenic coordinates.
Deprecated compatibility argument. The preferred setting is a fixed `exponential_waning` row in `par_tab` when using a parameter table.
A data frame with `sample_times`, `biomarker_ids`, and `antibody_level` columns.
data(example_antigenic_map)
simulate_antibody_model(c("boost_long"=2,"boost_short"=3,"boost_delay"=1,"wane_short"=0.2,"wane_long"=0.01, "antigenic_seniority"=0,"cr_long"=0.1,"cr_short"=0.03), times=example_antigenic_map$inf_times,infection_history=NULL,antigenic_map=example_antigenic_map)
#> sample_times biomarker_ids antibody_level
#> 1 1968 1968 0.00000000
#> 2 1968 1969 0.00000000
#> 3 1968 1970 0.00000000
#> 4 1968 1971 0.00000000
#> 5 1968 1972 0.00000000
#> 6 1968 1973 0.00000000
#> 7 1968 1974 0.00000000
#> 8 1968 1975 0.00000000
#> 9 1968 1976 0.00000000
#> 10 1968 1977 0.00000000
#> 11 1968 1978 0.00000000
#> 12 1968 1979 0.00000000
#> 13 1968 1980 0.00000000
#> 14 1968 1981 0.00000000
#> 15 1968 1982 0.00000000
#> 16 1968 1983 0.00000000
#> 17 1968 1984 0.00000000
#> 18 1968 1985 0.00000000
#> 19 1968 1986 0.00000000
#> 20 1968 1987 0.00000000
#> 21 1968 1988 0.00000000
#> 22 1968 1989 0.00000000
#> 23 1968 1990 0.00000000
#> 24 1968 1991 0.00000000
#> 25 1968 1992 0.00000000
#> 26 1968 1993 0.00000000
#> 27 1968 1994 0.00000000
#> 28 1968 1995 0.00000000
#> 29 1968 1996 0.00000000
#> 30 1968 1997 0.00000000
#> 31 1968 1998 0.00000000
#> 32 1968 1999 0.00000000
#> 33 1968 2000 0.00000000
#> 34 1968 2001 0.00000000
#> 35 1968 2002 0.00000000
#> 36 1968 2003 0.00000000
#> 37 1968 2004 0.00000000
#> 38 1968 2005 0.00000000
#> 39 1968 2006 0.00000000
#> 40 1968 2007 0.00000000
#> 41 1968 2008 0.00000000
#> 42 1968 2009 0.00000000
#> 43 1968 2010 0.00000000
#> 44 1968 2011 0.00000000
#> 45 1968 2012 0.00000000
#> 46 1968 2013 0.00000000
#> 47 1968 2014 0.00000000
#> 48 1968 2015 0.00000000
#> 49 1969 1968 5.00000000
#> 50 1969 1969 4.65580237
#> 51 1969 1970 4.31891394
#> 52 1969 1971 3.99269626
#> 53 1969 1972 3.67685615
#> 54 1969 1973 3.37003931
#> 55 1969 1974 3.07073576
#> 56 1969 1975 2.77903042
#> 57 1969 1976 2.50196763
#> 58 1969 1977 2.25463971
#> 59 1969 1978 2.08384098
#> 60 1969 1979 2.03094039
#> 61 1969 1980 1.98493776
#> 62 1969 1981 1.94123327
#> 63 1969 1982 1.89596503
#> 64 1969 1983 1.84621326
#> 65 1969 1984 1.79002991
#> 66 1969 1985 1.72664066
#> 67 1969 1986 1.65697412
#> 68 1969 1987 1.58342035
#> 69 1969 1988 1.50871694
#> 70 1969 1989 1.43430156
#> 71 1969 1990 1.35905333
#> 72 1969 1991 1.28066510
#> 73 1969 1992 1.19767313
#> 74 1969 1993 1.11059151
#> 75 1969 1994 1.02129061
#> 76 1969 1995 0.93192798
#> 77 1969 1996 0.84458960
#> 78 1969 1997 0.76117440
#> 79 1969 1998 0.68340387
#> 80 1969 1999 0.61320308
#> 81 1969 2000 0.55192890
#> 82 1969 2001 0.49673547
#> 83 1969 2002 0.44021500
#> 84 1969 2003 0.37669525
#> 85 1969 2004 0.30648322
#> 86 1969 2005 0.23229761
#> 87 1969 2006 0.15597455
#> 88 1969 2007 0.07843396
#> 89 1969 2008 0.00000000
#> 90 1969 2009 0.00000000
#> 91 1969 2010 0.00000000
#> 92 1969 2011 0.00000000
#> 93 1969 2012 0.00000000
#> 94 1969 2013 0.00000000
#> 95 1969 2014 0.00000000
#> 96 1969 2015 0.00000000
#> 97 1970 1968 4.38000000
#> 98 1970 1969 4.05954014
#> 99 1970 1970 3.74588539
#> 100 1970 1971 3.44216548
#> 101 1970 1972 3.14810745
#> 102 1970 1973 2.86245039
#> 103 1970 1974 2.58378846
#> 104 1970 1975 2.31220074
#> 105 1970 1976 2.05424572
#> 106 1970 1977 1.82397490
#> 107 1970 1978 1.66707279
#> 108 1970 1979 1.62475231
#> 109 1970 1980 1.58795021
#> 110 1970 1981 1.55298662
#> 111 1970 1982 1.51677203
#> 112 1970 1983 1.47697061
#> 113 1970 1984 1.43202393
#> 114 1970 1985 1.38131253
#> 115 1970 1986 1.32557930
#> 116 1970 1987 1.26673628
#> 117 1970 1988 1.20697355
#> 118 1970 1989 1.14744125
#> 119 1970 1990 1.08724266
#> 120 1970 1991 1.02453208
#> 121 1970 1992 0.95813850
#> 122 1970 1993 0.88847320
#> 123 1970 1994 0.81703249
#> 124 1970 1995 0.74554238
#> 125 1970 1996 0.67567168
#> 126 1970 1997 0.60893952
#> 127 1970 1998 0.54672310
#> 128 1970 1999 0.49056246
#> 129 1970 2000 0.44154312
#> 130 1970 2001 0.39738837
#> 131 1970 2002 0.35217200
#> 132 1970 2003 0.30135620
#> 133 1970 2004 0.24518657
#> 134 1970 2005 0.18583809
#> 135 1970 2006 0.12477964
#> 136 1970 2007 0.06274717
#> 137 1970 2008 0.00000000
#> 138 1970 2009 0.00000000
#> 139 1970 2010 0.00000000
#> 140 1970 2011 0.00000000
#> 141 1970 2012 0.00000000
#> 142 1970 2013 0.00000000
#> 143 1970 2014 0.00000000
#> 144 1970 2015 0.00000000
#> 145 1971 1968 3.76000000
#> 146 1971 1969 3.46327791
#> 147 1971 1970 3.17285684
#> 148 1971 1971 2.89163471
#> 149 1971 1972 2.61935875
#> 150 1971 1973 2.35486147
#> 151 1971 1974 2.09684117
#> 152 1971 1975 1.84537105
#> 153 1971 1976 1.60652382
#> 154 1971 1977 1.39331010
#> 155 1971 1978 1.25030459
#> 156 1971 1979 1.21856423
#> 157 1971 1980 1.19096266
#> 158 1971 1981 1.16473996
#> 159 1971 1982 1.13757902
#> 160 1971 1983 1.10772796
#> 161 1971 1984 1.07401795
#> 162 1971 1985 1.03598440
#> 163 1971 1986 0.99418447
#> 164 1971 1987 0.95005221
#> 165 1971 1988 0.90523017
#> 166 1971 1989 0.86058093
#> 167 1971 1990 0.81543200
#> 168 1971 1991 0.76839906
#> 169 1971 1992 0.71860388
#> 170 1971 1993 0.66635490
#> 171 1971 1994 0.61277437
#> 172 1971 1995 0.55915679
#> 173 1971 1996 0.50675376
#> 174 1971 1997 0.45670464
#> 175 1971 1998 0.41004232
#> 176 1971 1999 0.36792185
#> 177 1971 2000 0.33115734
#> 178 1971 2001 0.29804128
#> 179 1971 2002 0.26412900
#> 180 1971 2003 0.22601715
#> 181 1971 2004 0.18388993
#> 182 1971 2005 0.13937856
#> 183 1971 2006 0.09358473
#> 184 1971 2007 0.04706038
#> 185 1971 2008 0.00000000
#> 186 1971 2009 0.00000000
#> 187 1971 2010 0.00000000
#> 188 1971 2011 0.00000000
#> 189 1971 2012 0.00000000
#> 190 1971 2013 0.00000000
#> 191 1971 2014 0.00000000
#> 192 1971 2015 0.00000000
#> 193 1972 1968 3.14000000
#> 194 1972 1969 2.86701567
#> 195 1972 1970 2.59982829
#> 196 1972 1971 2.34110393
#> 197 1972 1972 2.09061005
#> 198 1972 1973 1.84727256
#> 199 1972 1974 1.60989388
#> 200 1972 1975 1.37854137
#> 201 1972 1976 1.15880191
#> 202 1972 1977 0.96264529
#> 203 1972 1978 0.83353639
#> 204 1972 1979 0.81237616
#> 205 1972 1980 0.79397510
#> 206 1972 1981 0.77649331
#> 207 1972 1982 0.75838601
#> 208 1972 1983 0.73848530
#> 209 1972 1984 0.71601197
#> 210 1972 1985 0.69065626
#> 211 1972 1986 0.66278965
#> 212 1972 1987 0.63336814
#> 213 1972 1988 0.60348678
#> 214 1972 1989 0.57372062
#> 215 1972 1990 0.54362133
#> 216 1972 1991 0.51226604
#> 217 1972 1992 0.47906925
#> 218 1972 1993 0.44423660
#> 219 1972 1994 0.40851624
#> 220 1972 1995 0.37277119
#> 221 1972 1996 0.33783584
#> 222 1972 1997 0.30446976
#> 223 1972 1998 0.27336155
#> 224 1972 1999 0.24528123
#> 225 1972 2000 0.22077156
#> 226 1972 2001 0.19869419
#> 227 1972 2002 0.17608600
#> 228 1972 2003 0.15067810
#> 229 1972 2004 0.12259329
#> 230 1972 2005 0.09291904
#> 231 1972 2006 0.06238982
#> 232 1972 2007 0.03137359
#> 233 1972 2008 0.00000000
#> 234 1972 2009 0.00000000
#> 235 1972 2010 0.00000000
#> 236 1972 2011 0.00000000
#> 237 1972 2012 0.00000000
#> 238 1972 2013 0.00000000
#> 239 1972 2014 0.00000000
#> 240 1972 2015 0.00000000
#> 241 1973 1968 2.52000000
#> 242 1973 1969 2.27075344
#> 243 1973 1970 2.02679975
#> 244 1973 1971 1.79057315
#> 245 1973 1972 1.56186135
#> 246 1973 1973 1.33968364
#> 247 1973 1974 1.12294658
#> 248 1973 1975 0.91171169
#> 249 1973 1976 0.71108001
#> 250 1973 1977 0.53198048
#> 251 1973 1978 0.41676820
#> 252 1973 1979 0.40618808
#> 253 1973 1980 0.39698755
#> 254 1973 1981 0.38824665
#> 255 1973 1982 0.37919301
#> 256 1973 1983 0.36924265
#> 257 1973 1984 0.35800598
#> 258 1973 1985 0.34532813
#> 259 1973 1986 0.33139482
#> 260 1973 1987 0.31668407
#> 261 1973 1988 0.30174339
#> 262 1973 1989 0.28686031
#> 263 1973 1990 0.27181067
#> 264 1973 1991 0.25613302
#> 265 1973 1992 0.23953463
#> 266 1973 1993 0.22211830
#> 267 1973 1994 0.20425812
#> 268 1973 1995 0.18638560
#> 269 1973 1996 0.16891792
#> 270 1973 1997 0.15223488
#> 271 1973 1998 0.13668077
#> 272 1973 1999 0.12264062
#> 273 1973 2000 0.11038578
#> 274 1973 2001 0.09934709
#> 275 1973 2002 0.08804300
#> 276 1973 2003 0.07533905
#> 277 1973 2004 0.06129664
#> 278 1973 2005 0.04645952
#> 279 1973 2006 0.03119491
#> 280 1973 2007 0.01568679
#> 281 1973 2008 0.00000000
#> 282 1973 2009 0.00000000
#> 283 1973 2010 0.00000000
#> 284 1973 2011 0.00000000
#> 285 1973 2012 0.00000000
#> 286 1973 2013 0.00000000
#> 287 1973 2014 0.00000000
#> 288 1973 2015 0.00000000
#> 289 1974 1968 1.90000000
#> 290 1974 1969 1.67449121
#> 291 1974 1970 1.45377120
#> 292 1974 1971 1.24004238
#> 293 1974 1972 1.03311265
#> 294 1974 1973 0.83209472
#> 295 1974 1974 0.63599929
#> 296 1974 1975 0.44488200
#> 297 1974 1976 0.26335810
#> 298 1974 1977 0.10131567
#> 299 1974 1978 0.00000000
#> 300 1974 1979 0.00000000
#> 301 1974 1980 0.00000000
#> 302 1974 1981 0.00000000
#> 303 1974 1982 0.00000000
#> 304 1974 1983 0.00000000
#> 305 1974 1984 0.00000000
#> 306 1974 1985 0.00000000
#> 307 1974 1986 0.00000000
#> 308 1974 1987 0.00000000
#> 309 1974 1988 0.00000000
#> 310 1974 1989 0.00000000
#> 311 1974 1990 0.00000000
#> 312 1974 1991 0.00000000
#> 313 1974 1992 0.00000000
#> 314 1974 1993 0.00000000
#> 315 1974 1994 0.00000000
#> 316 1974 1995 0.00000000
#> 317 1974 1996 0.00000000
#> 318 1974 1997 0.00000000
#> 319 1974 1998 0.00000000
#> 320 1974 1999 0.00000000
#> 321 1974 2000 0.00000000
#> 322 1974 2001 0.00000000
#> 323 1974 2002 0.00000000
#> 324 1974 2003 0.00000000
#> 325 1974 2004 0.00000000
#> 326 1974 2005 0.00000000
#> 327 1974 2006 0.00000000
#> 328 1974 2007 0.00000000
#> 329 1974 2008 0.00000000
#> 330 1974 2009 0.00000000
#> 331 1974 2010 0.00000000
#> 332 1974 2011 0.00000000
#> 333 1974 2012 0.00000000
#> 334 1974 2013 0.00000000
#> 335 1974 2014 0.00000000
#> 336 1974 2015 0.00000000
#> 337 1975 1968 1.88000000
#> 338 1975 1969 1.65686498
#> 339 1975 1970 1.43846835
#> 340 1975 1971 1.22698930
#> 341 1975 1972 1.02223778
#> 342 1975 1973 0.82333583
#> 343 1975 1974 0.62930456
#> 344 1975 1975 0.44019903
#> 345 1975 1976 0.26058591
#> 346 1975 1977 0.10024919
#> 347 1975 1978 0.00000000
#> 348 1975 1979 0.00000000
#> 349 1975 1980 0.00000000
#> 350 1975 1981 0.00000000
#> 351 1975 1982 0.00000000
#> 352 1975 1983 0.00000000
#> 353 1975 1984 0.00000000
#> 354 1975 1985 0.00000000
#> 355 1975 1986 0.00000000
#> 356 1975 1987 0.00000000
#> 357 1975 1988 0.00000000
#> 358 1975 1989 0.00000000
#> 359 1975 1990 0.00000000
#> 360 1975 1991 0.00000000
#> 361 1975 1992 0.00000000
#> 362 1975 1993 0.00000000
#> 363 1975 1994 0.00000000
#> 364 1975 1995 0.00000000
#> 365 1975 1996 0.00000000
#> 366 1975 1997 0.00000000
#> 367 1975 1998 0.00000000
#> 368 1975 1999 0.00000000
#> 369 1975 2000 0.00000000
#> 370 1975 2001 0.00000000
#> 371 1975 2002 0.00000000
#> 372 1975 2003 0.00000000
#> 373 1975 2004 0.00000000
#> 374 1975 2005 0.00000000
#> 375 1975 2006 0.00000000
#> 376 1975 2007 0.00000000
#> 377 1975 2008 0.00000000
#> 378 1975 2009 0.00000000
#> 379 1975 2010 0.00000000
#> 380 1975 2011 0.00000000
#> 381 1975 2012 0.00000000
#> 382 1975 2013 0.00000000
#> 383 1975 2014 0.00000000
#> 384 1975 2015 0.00000000
#> 385 1976 1968 1.86000000
#> 386 1976 1969 1.63923876
#> 387 1976 1970 1.42316549
#> 388 1976 1971 1.21393622
#> 389 1976 1972 1.01136291
#> 390 1976 1973 0.81457694
#> 391 1976 1974 0.62260983
#> 392 1976 1975 0.43551606
#> 393 1976 1976 0.25781372
#> 394 1976 1977 0.09918271
#> 395 1976 1978 0.00000000
#> 396 1976 1979 0.00000000
#> 397 1976 1980 0.00000000
#> 398 1976 1981 0.00000000
#> 399 1976 1982 0.00000000
#> 400 1976 1983 0.00000000
#> 401 1976 1984 0.00000000
#> 402 1976 1985 0.00000000
#> 403 1976 1986 0.00000000
#> 404 1976 1987 0.00000000
#> 405 1976 1988 0.00000000
#> 406 1976 1989 0.00000000
#> 407 1976 1990 0.00000000
#> 408 1976 1991 0.00000000
#> 409 1976 1992 0.00000000
#> 410 1976 1993 0.00000000
#> 411 1976 1994 0.00000000
#> 412 1976 1995 0.00000000
#> 413 1976 1996 0.00000000
#> 414 1976 1997 0.00000000
#> 415 1976 1998 0.00000000
#> 416 1976 1999 0.00000000
#> 417 1976 2000 0.00000000
#> 418 1976 2001 0.00000000
#> 419 1976 2002 0.00000000
#> 420 1976 2003 0.00000000
#> 421 1976 2004 0.00000000
#> 422 1976 2005 0.00000000
#> 423 1976 2006 0.00000000
#> 424 1976 2007 0.00000000
#> 425 1976 2008 0.00000000
#> 426 1976 2009 0.00000000
#> 427 1976 2010 0.00000000
#> 428 1976 2011 0.00000000
#> 429 1976 2012 0.00000000
#> 430 1976 2013 0.00000000
#> 431 1976 2014 0.00000000
#> 432 1976 2015 0.00000000
#> 433 1977 1968 1.84000000
#> 434 1977 1969 1.62161254
#> 435 1977 1970 1.40786264
#> 436 1977 1971 1.20088314
#> 437 1977 1972 1.00048804
#> 438 1977 1973 0.80581804
#> 439 1977 1974 0.61591510
#> 440 1977 1975 0.43083310
#> 441 1977 1976 0.25504153
#> 442 1977 1977 0.09811623
#> 443 1977 1978 0.00000000
#> 444 1977 1979 0.00000000
#> 445 1977 1980 0.00000000
#> 446 1977 1981 0.00000000
#> 447 1977 1982 0.00000000
#> 448 1977 1983 0.00000000
#> 449 1977 1984 0.00000000
#> 450 1977 1985 0.00000000
#> 451 1977 1986 0.00000000
#> 452 1977 1987 0.00000000
#> 453 1977 1988 0.00000000
#> 454 1977 1989 0.00000000
#> 455 1977 1990 0.00000000
#> 456 1977 1991 0.00000000
#> 457 1977 1992 0.00000000
#> 458 1977 1993 0.00000000
#> 459 1977 1994 0.00000000
#> 460 1977 1995 0.00000000
#> 461 1977 1996 0.00000000
#> 462 1977 1997 0.00000000
#> 463 1977 1998 0.00000000
#> 464 1977 1999 0.00000000
#> 465 1977 2000 0.00000000
#> 466 1977 2001 0.00000000
#> 467 1977 2002 0.00000000
#> 468 1977 2003 0.00000000
#> 469 1977 2004 0.00000000
#> 470 1977 2005 0.00000000
#> 471 1977 2006 0.00000000
#> 472 1977 2007 0.00000000
#> 473 1977 2008 0.00000000
#> 474 1977 2009 0.00000000
#> 475 1977 2010 0.00000000
#> 476 1977 2011 0.00000000
#> 477 1977 2012 0.00000000
#> 478 1977 2013 0.00000000
#> 479 1977 2014 0.00000000
#> 480 1977 2015 0.00000000
#> 481 1978 1968 1.82000000
#> 482 1978 1969 1.60398632
#> 483 1978 1970 1.39255978
#> 484 1978 1971 1.18783007
#> 485 1978 1972 0.98961317
#> 486 1978 1973 0.79705915
#> 487 1978 1974 0.60922037
#> 488 1978 1975 0.42615013
#> 489 1978 1976 0.25226934
#> 490 1978 1977 0.09704975
#> 491 1978 1978 0.00000000
#> 492 1978 1979 0.00000000
#> 493 1978 1980 0.00000000
#> 494 1978 1981 0.00000000
#> 495 1978 1982 0.00000000
#> 496 1978 1983 0.00000000
#> 497 1978 1984 0.00000000
#> 498 1978 1985 0.00000000
#> 499 1978 1986 0.00000000
#> 500 1978 1987 0.00000000
#> 501 1978 1988 0.00000000
#> 502 1978 1989 0.00000000
#> 503 1978 1990 0.00000000
#> 504 1978 1991 0.00000000
#> 505 1978 1992 0.00000000
#> 506 1978 1993 0.00000000
#> 507 1978 1994 0.00000000
#> 508 1978 1995 0.00000000
#> 509 1978 1996 0.00000000
#> 510 1978 1997 0.00000000
#> 511 1978 1998 0.00000000
#> 512 1978 1999 0.00000000
#> 513 1978 2000 0.00000000
#> 514 1978 2001 0.00000000
#> 515 1978 2002 0.00000000
#> 516 1978 2003 0.00000000
#> 517 1978 2004 0.00000000
#> 518 1978 2005 0.00000000
#> 519 1978 2006 0.00000000
#> 520 1978 2007 0.00000000
#> 521 1978 2008 0.00000000
#> 522 1978 2009 0.00000000
#> 523 1978 2010 0.00000000
#> 524 1978 2011 0.00000000
#> 525 1978 2012 0.00000000
#> 526 1978 2013 0.00000000
#> 527 1978 2014 0.00000000
#> 528 1978 2015 0.00000000
#> 529 1979 1968 1.80000000
#> 530 1979 1969 1.58636009
#> 531 1979 1970 1.37725693
#> 532 1979 1971 1.17477699
#> 533 1979 1972 0.97873830
#> 534 1979 1973 0.78830026
#> 535 1979 1974 0.60252564
#> 536 1979 1975 0.42146716
#> 537 1979 1976 0.24949715
#> 538 1979 1977 0.09598327
#> 539 1979 1978 0.00000000
#> 540 1979 1979 0.00000000
#> 541 1979 1980 0.00000000
#> 542 1979 1981 0.00000000
#> 543 1979 1982 0.00000000
#> 544 1979 1983 0.00000000
#> 545 1979 1984 0.00000000
#> 546 1979 1985 0.00000000
#> 547 1979 1986 0.00000000
#> 548 1979 1987 0.00000000
#> 549 1979 1988 0.00000000
#> 550 1979 1989 0.00000000
#> 551 1979 1990 0.00000000
#> 552 1979 1991 0.00000000
#> 553 1979 1992 0.00000000
#> 554 1979 1993 0.00000000
#> 555 1979 1994 0.00000000
#> 556 1979 1995 0.00000000
#> 557 1979 1996 0.00000000
#> 558 1979 1997 0.00000000
#> 559 1979 1998 0.00000000
#> 560 1979 1999 0.00000000
#> 561 1979 2000 0.00000000
#> 562 1979 2001 0.00000000
#> 563 1979 2002 0.00000000
#> 564 1979 2003 0.00000000
#> 565 1979 2004 0.00000000
#> 566 1979 2005 0.00000000
#> 567 1979 2006 0.00000000
#> 568 1979 2007 0.00000000
#> 569 1979 2008 0.00000000
#> 570 1979 2009 0.00000000
#> 571 1979 2010 0.00000000
#> 572 1979 2011 0.00000000
#> 573 1979 2012 0.00000000
#> 574 1979 2013 0.00000000
#> 575 1979 2014 0.00000000
#> 576 1979 2015 0.00000000
#> 577 1980 1968 1.78000000
#> 578 1980 1969 1.56873387
#> 579 1980 1970 1.36195407
#> 580 1980 1971 1.16172391
#> 581 1980 1972 0.96786343
#> 582 1980 1973 0.77954137
#> 583 1980 1974 0.59583091
#> 584 1980 1975 0.41678419
#> 585 1980 1976 0.24672496
#> 586 1980 1977 0.09491679
#> 587 1980 1978 0.00000000
#> 588 1980 1979 0.00000000
#> 589 1980 1980 0.00000000
#> 590 1980 1981 0.00000000
#> 591 1980 1982 0.00000000
#> 592 1980 1983 0.00000000
#> 593 1980 1984 0.00000000
#> 594 1980 1985 0.00000000
#> 595 1980 1986 0.00000000
#> 596 1980 1987 0.00000000
#> 597 1980 1988 0.00000000
#> 598 1980 1989 0.00000000
#> 599 1980 1990 0.00000000
#> 600 1980 1991 0.00000000
#> 601 1980 1992 0.00000000
#> 602 1980 1993 0.00000000
#> 603 1980 1994 0.00000000
#> 604 1980 1995 0.00000000
#> 605 1980 1996 0.00000000
#> 606 1980 1997 0.00000000
#> 607 1980 1998 0.00000000
#> 608 1980 1999 0.00000000
#> 609 1980 2000 0.00000000
#> 610 1980 2001 0.00000000
#> 611 1980 2002 0.00000000
#> 612 1980 2003 0.00000000
#> 613 1980 2004 0.00000000
#> 614 1980 2005 0.00000000
#> 615 1980 2006 0.00000000
#> 616 1980 2007 0.00000000
#> 617 1980 2008 0.00000000
#> 618 1980 2009 0.00000000
#> 619 1980 2010 0.00000000
#> 620 1980 2011 0.00000000
#> 621 1980 2012 0.00000000
#> 622 1980 2013 0.00000000
#> 623 1980 2014 0.00000000
#> 624 1980 2015 0.00000000
#> 625 1981 1968 1.76000000
#> 626 1981 1969 1.55110765
#> 627 1981 1970 1.34665122
#> 628 1981 1971 1.14867083
#> 629 1981 1972 0.95698856
#> 630 1981 1973 0.77078248
#> 631 1981 1974 0.58913618
#> 632 1981 1975 0.41210122
#> 633 1981 1976 0.24395277
#> 634 1981 1977 0.09385031
#> 635 1981 1978 0.00000000
#> 636 1981 1979 0.00000000
#> 637 1981 1980 0.00000000
#> 638 1981 1981 0.00000000
#> 639 1981 1982 0.00000000
#> 640 1981 1983 0.00000000
#> 641 1981 1984 0.00000000
#> 642 1981 1985 0.00000000
#> 643 1981 1986 0.00000000
#> 644 1981 1987 0.00000000
#> 645 1981 1988 0.00000000
#> 646 1981 1989 0.00000000
#> 647 1981 1990 0.00000000
#> 648 1981 1991 0.00000000
#> 649 1981 1992 0.00000000
#> 650 1981 1993 0.00000000
#> 651 1981 1994 0.00000000
#> 652 1981 1995 0.00000000
#> 653 1981 1996 0.00000000
#> 654 1981 1997 0.00000000
#> 655 1981 1998 0.00000000
#> 656 1981 1999 0.00000000
#> 657 1981 2000 0.00000000
#> 658 1981 2001 0.00000000
#> 659 1981 2002 0.00000000
#> 660 1981 2003 0.00000000
#> 661 1981 2004 0.00000000
#> 662 1981 2005 0.00000000
#> 663 1981 2006 0.00000000
#> 664 1981 2007 0.00000000
#> 665 1981 2008 0.00000000
#> 666 1981 2009 0.00000000
#> 667 1981 2010 0.00000000
#> 668 1981 2011 0.00000000
#> 669 1981 2012 0.00000000
#> 670 1981 2013 0.00000000
#> 671 1981 2014 0.00000000
#> 672 1981 2015 0.00000000
#> 673 1982 1968 1.74000000
#> 674 1982 1969 1.53348142
#> 675 1982 1970 1.33134836
#> 676 1982 1971 1.13561776
#> 677 1982 1972 0.94611369
#> 678 1982 1973 0.76202359
#> 679 1982 1974 0.58244145
#> 680 1982 1975 0.40741825
#> 681 1982 1976 0.24118058
#> 682 1982 1977 0.09278383
#> 683 1982 1978 0.00000000
#> 684 1982 1979 0.00000000
#> 685 1982 1980 0.00000000
#> 686 1982 1981 0.00000000
#> 687 1982 1982 0.00000000
#> 688 1982 1983 0.00000000
#> 689 1982 1984 0.00000000
#> 690 1982 1985 0.00000000
#> 691 1982 1986 0.00000000
#> 692 1982 1987 0.00000000
#> 693 1982 1988 0.00000000
#> 694 1982 1989 0.00000000
#> 695 1982 1990 0.00000000
#> 696 1982 1991 0.00000000
#> 697 1982 1992 0.00000000
#> 698 1982 1993 0.00000000
#> 699 1982 1994 0.00000000
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#> 2138 2012 1993 0.00000000
#> 2139 2012 1994 0.00000000
#> 2140 2012 1995 0.00000000
#> 2141 2012 1996 0.00000000
#> 2142 2012 1997 0.00000000
#> 2143 2012 1998 0.00000000
#> 2144 2012 1999 0.00000000
#> 2145 2012 2000 0.00000000
#> 2146 2012 2001 0.00000000
#> 2147 2012 2002 0.00000000
#> 2148 2012 2003 0.00000000
#> 2149 2012 2004 0.00000000
#> 2150 2012 2005 0.00000000
#> 2151 2012 2006 0.00000000
#> 2152 2012 2007 0.00000000
#> 2153 2012 2008 0.00000000
#> 2154 2012 2009 0.00000000
#> 2155 2012 2010 0.00000000
#> 2156 2012 2011 0.00000000
#> 2157 2012 2012 0.00000000
#> 2158 2012 2013 0.00000000
#> 2159 2012 2014 0.00000000
#> 2160 2012 2015 0.00000000
#> 2161 2013 1968 1.12000000
#> 2162 2013 1969 0.98706850
#> 2163 2013 1970 0.85695987
#> 2164 2013 1971 0.73097235
#> 2165 2013 1972 0.60899272
#> 2166 2013 1973 0.49049794
#> 2167 2013 1974 0.37490484
#> 2168 2013 1975 0.26224623
#> 2169 2013 1976 0.15524267
#> 2170 2013 1977 0.05972292
#> 2171 2013 1978 0.00000000
#> 2172 2013 1979 0.00000000
#> 2173 2013 1980 0.00000000
#> 2174 2013 1981 0.00000000
#> 2175 2013 1982 0.00000000
#> 2176 2013 1983 0.00000000
#> 2177 2013 1984 0.00000000
#> 2178 2013 1985 0.00000000
#> 2179 2013 1986 0.00000000
#> 2180 2013 1987 0.00000000
#> 2181 2013 1988 0.00000000
#> 2182 2013 1989 0.00000000
#> 2183 2013 1990 0.00000000
#> 2184 2013 1991 0.00000000
#> 2185 2013 1992 0.00000000
#> 2186 2013 1993 0.00000000
#> 2187 2013 1994 0.00000000
#> 2188 2013 1995 0.00000000
#> 2189 2013 1996 0.00000000
#> 2190 2013 1997 0.00000000
#> 2191 2013 1998 0.00000000
#> 2192 2013 1999 0.00000000
#> 2193 2013 2000 0.00000000
#> 2194 2013 2001 0.00000000
#> 2195 2013 2002 0.00000000
#> 2196 2013 2003 0.00000000
#> 2197 2013 2004 0.00000000
#> 2198 2013 2005 0.00000000
#> 2199 2013 2006 0.00000000
#> 2200 2013 2007 0.00000000
#> 2201 2013 2008 0.00000000
#> 2202 2013 2009 0.00000000
#> 2203 2013 2010 0.00000000
#> 2204 2013 2011 0.00000000
#> 2205 2013 2012 0.00000000
#> 2206 2013 2013 0.00000000
#> 2207 2013 2014 0.00000000
#> 2208 2013 2015 0.00000000
#> 2209 2014 1968 1.10000000
#> 2210 2014 1969 0.96944228
#> 2211 2014 1970 0.84165701
#> 2212 2014 1971 0.71791927
#> 2213 2014 1972 0.59811785
#> 2214 2014 1973 0.48173905
#> 2215 2014 1974 0.36821011
#> 2216 2014 1975 0.25756326
#> 2217 2014 1976 0.15247048
#> 2218 2014 1977 0.05865644
#> 2219 2014 1978 0.00000000
#> 2220 2014 1979 0.00000000
#> 2221 2014 1980 0.00000000
#> 2222 2014 1981 0.00000000
#> 2223 2014 1982 0.00000000
#> 2224 2014 1983 0.00000000
#> 2225 2014 1984 0.00000000
#> 2226 2014 1985 0.00000000
#> 2227 2014 1986 0.00000000
#> 2228 2014 1987 0.00000000
#> 2229 2014 1988 0.00000000
#> 2230 2014 1989 0.00000000
#> 2231 2014 1990 0.00000000
#> 2232 2014 1991 0.00000000
#> 2233 2014 1992 0.00000000
#> 2234 2014 1993 0.00000000
#> 2235 2014 1994 0.00000000
#> 2236 2014 1995 0.00000000
#> 2237 2014 1996 0.00000000
#> 2238 2014 1997 0.00000000
#> 2239 2014 1998 0.00000000
#> 2240 2014 1999 0.00000000
#> 2241 2014 2000 0.00000000
#> 2242 2014 2001 0.00000000
#> 2243 2014 2002 0.00000000
#> 2244 2014 2003 0.00000000
#> 2245 2014 2004 0.00000000
#> 2246 2014 2005 0.00000000
#> 2247 2014 2006 0.00000000
#> 2248 2014 2007 0.00000000
#> 2249 2014 2008 0.00000000
#> 2250 2014 2009 0.00000000
#> 2251 2014 2010 0.00000000
#> 2252 2014 2011 0.00000000
#> 2253 2014 2012 0.00000000
#> 2254 2014 2013 0.00000000
#> 2255 2014 2014 0.00000000
#> 2256 2014 2015 0.00000000
#> 2257 2015 1968 1.08000000
#> 2258 2015 1969 0.95181606
#> 2259 2015 1970 0.82635416
#> 2260 2015 1971 0.70486619
#> 2261 2015 1972 0.58724298
#> 2262 2015 1973 0.47298016
#> 2263 2015 1974 0.36151538
#> 2264 2015 1975 0.25288030
#> 2265 2015 1976 0.14969829
#> 2266 2015 1977 0.05758996
#> 2267 2015 1978 0.00000000
#> 2268 2015 1979 0.00000000
#> 2269 2015 1980 0.00000000
#> 2270 2015 1981 0.00000000
#> 2271 2015 1982 0.00000000
#> 2272 2015 1983 0.00000000
#> 2273 2015 1984 0.00000000
#> 2274 2015 1985 0.00000000
#> 2275 2015 1986 0.00000000
#> 2276 2015 1987 0.00000000
#> 2277 2015 1988 0.00000000
#> 2278 2015 1989 0.00000000
#> 2279 2015 1990 0.00000000
#> 2280 2015 1991 0.00000000
#> 2281 2015 1992 0.00000000
#> 2282 2015 1993 0.00000000
#> 2283 2015 1994 0.00000000
#> 2284 2015 1995 0.00000000
#> 2285 2015 1996 0.00000000
#> 2286 2015 1997 0.00000000
#> 2287 2015 1998 0.00000000
#> 2288 2015 1999 0.00000000
#> 2289 2015 2000 0.00000000
#> 2290 2015 2001 0.00000000
#> 2291 2015 2002 0.00000000
#> 2292 2015 2003 0.00000000
#> 2293 2015 2004 0.00000000
#> 2294 2015 2005 0.00000000
#> 2295 2015 2006 0.00000000
#> 2296 2015 2007 0.00000000
#> 2297 2015 2008 0.00000000
#> 2298 2015 2009 0.00000000
#> 2299 2015 2010 0.00000000
#> 2300 2015 2011 0.00000000
#> 2301 2015 2012 0.00000000
#> 2302 2015 2013 0.00000000
#> 2303 2015 2014 0.00000000
#> 2304 2015 2015 0.00000000