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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)
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)$bpar
endpoints(m)$distimes
}
\keyword{ manip }
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