% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/parent_solutions.R
\name{logistic.solution}
\alias{logistic.solution}
\title{Logistic kinetics}
\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}{Minimum rate constant effective at time zero.}

\item{r}{Growth rate of the increase in the rate constant.}
}
\value{
The value of the response variable at time \code{t}.
}
\description{
Function describing exponential decline from a defined starting value, with
an increasing rate constant, supposedly caused by microbial growth
}
\note{
The solution of the logistic model reduces to the
\code{\link{SFO.solution}} if \code{k0} is equal to \code{kmax}.
}
\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

}
\references{
FOCUS (2006) \dQuote{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,
\url{http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics}
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}
}
\seealso{
Other parent solutions: 
\code{\link{DFOP.solution}()},
\code{\link{FOMC.solution}()},
\code{\link{HS.solution}()},
\code{\link{IORE.solution}()},
\code{\link{SFO.solution}()},
\code{\link{SFORB.solution}()}
}
\concept{parent solutions}