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###############################################
## Soetaert and Herman (2008) ##
## A practical guide to ecological modelling ##
## Chapter 6. ##
## Model solution - numerical methods ##
## Chapter 6.6.1 ##
## The enzymatic reaction model ##
###############################################
#----------------------#
# the model equations: #
#----------------------#
model<-function(t,state,parameters){
with(as.list(c(state,parameters)),{ # unpack the state variables, parameters
dD <- -k1*E*D + k2*I
dI <- k1*E*D - k2*I - k3*I*F
dE <- -k1*E*D + k2*I + k3*I*F
dF <- - k3*I*F
dG <- k3*I*F
list(c(dD,dI,dE,dF,dG)) # the output, packed as a list
})
}
#-----------------------#
# the model parameters: #
#-----------------------#
parameters<-c(k1=0.01/24, # parameter values
k2=0.1/24,
k3=0.1/24)
#-------------------------#
# the initial conditions: #
#-------------------------#
state <-c(D=100, # state variable initial conditions
I=10,
E=1,
F=1,
G=0)
#----------------------#
# RUNNING the model: #
#----------------------#
times <-seq(0,300,0.5) # time: from 0 to 1000 hours, steps of 0.5 hours
# integrate the model
require(deSolve) # package with the integration routine:
out <-as.data.frame(ode(state,times,model,parameters))
#------------------------#
# PLOTTING model output: #
#------------------------#
#windows()
par(mfrow=c(2,2), oma=c(0,0,3,0)) # set number of plots (mfrow) and margin size (oma)
plot (times,out$D,type="l",main="[D]",xlab="time, hours",ylab="mol/m3",lwd=2)
plot (times,out$F,type="l",main="[F]",xlab="time, hours",ylab="mol/m3",lwd=2)
plot (times,out$E,type="l",main="[E]",xlab="time, hours",ylab="mol/m3",lwd=2)
plot (times,out$I,type="l",main="[I]",xlab="time, hours",ylab="mol/m3",lwd=2)
mtext(outer=TRUE,side=3,"enzymatic reaction",cex=1.5)
#plot (times,out$sum,type="l",col="red")
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