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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 }

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