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)

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Arguments

t: Time.
parent_0: Starting value for the response variable at time zero.
kmax: Maximum rate constant.
k0: Minimum rate constant effective at time zero.
r: Growth rate of the increase in the rate constant.

Value

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The value of the response variable at time t.

Note

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

References

FOCUS (2006) “Guidance Document on Estimating Persistence -and Degradation Kinetics from Environmental Fate Studies on Pesticides in -EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, -EC Document Reference Sanco/10058/2005 version 2.0, 434 pp, -http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics -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)
-  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, quiet = TRUE)
-  plot_sep(m)
-
-  summary(m)$bpar
-#>              Estimate   se_notrans   t value       Pr(>t)        Lower
-#> parent_0 1.057896e+02 1.9023449590 55.610120 3.768360e-16 1.016451e+02
-#> kmax     6.398190e-02 0.0143201029  4.467978 3.841828e-04 3.929235e-02
-#> k0       1.612775e-04 0.0005866813  0.274898 3.940351e-01 5.846688e-08
-#> r        2.263946e-01 0.1718110662  1.317695 1.061043e-01 4.335843e-02
-#> sigma    5.332935e+00 0.9145907310  5.830952 4.036926e-05 3.340213e+00
-#>                Upper
-#> parent_0 109.9341588
-#> kmax       0.1041853
-#> k0         0.4448749
-#> r          1.1821120
-#> sigma      7.3256566
-  endpoints(m)$distimes
-#>            DT50     DT90  DT50_k0 DT50_kmax
-#> parent 36.86533 62.41511 4297.853  10.83349
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Arguments

Value

Note

References

See also

Examples