Add the logistic model

1 files changed, 68 insertions, 0 deletions

diff --git a/man/logistic.solution.Rd b/man/logistic.solution.Rd
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+\name{logistic.solution}
+\alias{logistic.solution}
+\title{ Logistic kinetics }
+\description{
+  Function describing exponential decline from a defined starting value, with 
+  an increasing rate constant, supposedly caused by microbial growth
+}
+\usage{
+logistic.solution(t, parent.0, kmax, k0, r)
+}
+\arguments{
+  \item{t}{ Time. }
+  \item{parent.0}{ Starting value for the response variable at time zero. }
+  \item{kmax}{ Maximum rate constant. }
+  \item{k0}{ Minumum rate constant effective at time zero. }
+  \item{r}{ Growth rate of the increase in the rate constant. }
+}
+\note{
+  The solution of the logistic model reduces to the
+  \code{\link{SFO.solution}} if \code{k0} is equal to
+  \code{kmax}.
+}
+\value{
+  The value of the response variable at time \code{t}.
+}
+\references{
+  FOCUS (2014) \dQuote{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
+  \url{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)
+  plot_sep(m)
+  summary(m)$bpar
+}
+\keyword{ manip }