From d89e3d22eb9dc383897b09e9c5aa1b57f65cdbf0 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 21 Feb 2019 14:34:45 +0100 Subject: Add the logistic model --- docs/reference/logistic.solution.html | 295 ++++++++++++++++++++++++++++++++++ 1 file changed, 295 insertions(+) create mode 100644 docs/reference/logistic.solution.html (limited to 'docs/reference/logistic.solution.html') diff --git a/docs/reference/logistic.solution.html b/docs/reference/logistic.solution.html new file mode 100644 index 00000000..b0ab72d7 --- /dev/null +++ b/docs/reference/logistic.solution.html @@ -0,0 +1,295 @@ + + + + + + + + +Logistic kinetics — logistic.solution • mkin + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Logistic kinetics

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Function describing exponential decline from a defined starting value, with + an increasing rate constant, supposedly caused by microbial growth

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logistic.solution(t, parent.0, kmax, k0, r)
+ +

Arguments

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t

Time.

parent.0

Starting value for the response variable at time zero.

kmax

Maximum rate constant.

k0

Minumum rate constant effective at time zero.

r

Growth rate of the increase in the rate constant.

+ +

Note

+ +

The solution of the logistic model reduces to the + SFO.solution if k0 is equal to + kmax.

+ +

Value

+ +

The value of the response variable at time t.

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References

+ +

FOCUS (2014) “Generic guidance for Estimating Persistence and + Degradation Kinetics from Environmental Fate Studies on Pesticides in EU + Registration” Report of the FOCUS Work Group on Degradation Kinetics, + Version 1.1, 18 December 2014 + http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics

+ + +

Examples

+ 
  # Reproduce the plot on page 57 of FOCUS (2014)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
+       from = 0, to = 100, ylim = c(0, 100),
+       xlab = "Time", ylab = "Residue")
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
+       from = 0, to = 100, add = TRUE, lty = 2, col = 2)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
+       from = 0, to = 100, add = TRUE, lty = 3, col = 3)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 4, col = 4)
  plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 5, col = 5)
  legend("topright", inset = 0.05,
+         legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
+                         ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
+         lty = 1:5, col = 1:5)

+  # Fit with synthetic data
+  logistic <- mkinmod(parent = mkinsub("logistic"))
+
+  sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+  parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
+  parms_logistic_optim <- c(parent_0 = 100, parms_logistic)
+  d_logistic <- mkinpredict(logistic,
+    parms_logistic, c(parent = 100),
+    sampling_times)
+  d_2_1 <- add_err(d_logistic,
+    sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
+    n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
+
+  m <- mkinfit("logistic", d_2_1)
#> Model cost at call  1 :  789.6044 
+#> Model cost at call  2 :  789.6043 
+#> Model cost at call  7 :  716.9934 
+#> Model cost at call  12 :  697.1186 
+#> Model cost at call  15 :  697.1185 
+#> Model cost at call  16 :  697.1184 
+#> Model cost at call  17 :  661.1574 
+#> Model cost at call  20 :  661.1573 
+#> Model cost at call  22 :  620.0542 
+#> Model cost at call  25 :  620.0541 
+#> Model cost at call  29 :  616.6874 
+#> Model cost at call  32 :  616.6874 
+#> Model cost at call  33 :  616.6874 
+#> Model cost at call  34 :  615.1671 
+#> Model cost at call  37 :  615.1671 
+#> Model cost at call  39 :  612.0795 
+#> Model cost at call  42 :  612.0795 
+#> Model cost at call  43 :  612.0795 
+#> Model cost at call  44 :  605.9119 
+#> Model cost at call  45 :  593.0433 
+#> Model cost at call  46 :  548.0815 
+#> Model cost at call  47 :  504.9062 
+#> Model cost at call  50 :  504.9061 
+#> Model cost at call  51 :  504.9061 
+#> Model cost at call  53 :  485.929 
+#> Model cost at call  55 :  485.929 
+#> Model cost at call  56 :  485.929 
+#> Model cost at call  58 :  485.241 
+#> Model cost at call  60 :  485.241 
+#> Model cost at call  61 :  485.2409 
+#> Model cost at call  62 :  485.2409 
+#> Model cost at call  63 :  484.0717 
+#> Model cost at call  69 :  483.9062 
+#> Model cost at call  74 :  483.5646 
+#> Model cost at call  79 :  483.4908 
+#> Model cost at call  84 :  483.4859 
+#> Model cost at call  85 :  483.4859 
+#> Model cost at call  89 :  483.4848 
+#> Model cost at call  90 :  483.4836 
+#> Model cost at call  92 :  483.4836 
+#> Model cost at call  94 :  483.4836 
+#> Model cost at call  97 :  483.4833 
+#> Model cost at call  100 :  483.4833 
+#> Model cost at call  105 :  483.4832 
+#> Model cost at call  108 :  483.4832 
+#> Model cost at call  114 :  483.4832 
+#> Model cost at call  128 :  483.4832 
+#> Optimisation by method Port successfully terminated.
  plot_sep(m)
  summary(m)$bpar
#>              Estimate   se_notrans    t value       Pr(>t)        Lower
+#> parent_0 1.057896e+02 2.3743105248 44.5559374 6.656664e-16 1.006602e+02
+#> kmax     6.398190e-02 0.0193490291  3.3067243 2.836921e-03 3.329058e-02
+#> k0       1.612775e-04 0.0009640761  0.1672871 4.348592e-01 3.972250e-10
+#> r        2.263946e-01 0.2822811886  0.8020181 2.184792e-01 1.531165e-02
+#>                Upper
+#> parent_0 110.9190170
+#> kmax       0.1229682
+#> k0        65.4803698
+#> r          3.3474197
+
+ +
+ + +
+ + + + + + -- cgit v1.2.1