jameson: This model proposed by Giménez and Dalgaard (2004). It...

In Ghayabh/predictive-microbiology: bacterialgrowth Package

Description

This model proposed by Giménez and Dalgaard (2004). It corresponds to the Jameson effect and predicts that one microorganism stops growing when the other has reached its maximum population density (MPD).

Usage

jameson(t, state, parameters)

Arguments

t	time vector
state	initial values of Q1 (physiological state of the first flora),Q2 (physiological state of the second flora), y1 (the flora population 1) and y2 (the flora population 2) for the first time value.
parameters	parameter list

Details

\begin{equation}\begin{aligned} &\frac{d N_{L m}}{d t}=α_{L m}(t) \cdot μ_{\max }^{L m} \cdot≤ft(1-\frac{N_{L m}}{N_{\max }^{L M}}\right) \cdot≤ft(1-\frac{N_{L A B}}{N_{\max }^{L 4 B}}\right)\\ &α_{L m}(t)=\frac{q_{L m}(t)}{1+q_{L m}(t)} ; \quad \frac{d q_{L m}}{d t}=μ_{\max }^{L m} \cdot q_{L m}(t) ; \quad N_{L m}(0)=N_{L m 0}\\ &\frac{d N_{L A B}}{d t}=α_{L A B}(t) \cdot μ_{\max }^{L A B} \cdot≤ft(1-\frac{N_{L A B}}{N_{\max }^{L A B}}\right) \cdot≤ft(1-\frac{N_{L_{m}}}{N_{\max }^{L_{m}}}\right)\\ &α_{L A B}(t)=\frac{q_{L A B}(t)}{1+q_{h, B}(t)} ; \quad \frac{d q_{A B}}{d t}=μ_{\max }^{L A B} \cdot q_{L A B}(t), \quad N_{L A B}(0)=N_{L A B 0} \end{aligned}\end{equation}

Value

dQ1,dQ2,dy1,dy2

Examples

library(deSolve)
K2=10
Q2=1/((1/exp(-K2))-1)
K1=2
Q1=1/((1/exp(-K1))-1)
state <- c(Q1=Q1,Q2=Q2,y1=1,y2=10)
time <- seq(from=0, to=200, by = 1)
parameters <- c(mumax1 = 0.14, mumax2=0.3, ymax1=100000,ymax2=10000000)
out <- ode(y = c(Q1=1/((1/exp(-2))-1),Q2=1/((1/exp(-10))-1),y1=1,y2=10),
times = seq(from=0, to=200, by = 1),
func = jameson, parms = c(mumax1 = 0.14, mumax2=0.3, ymax1=100000,ymax2=10000000))
plot(out)
plot(time,log10(out[,"y1"]),col="red", lwd = 2, lty = 1)
plot(time,log10(out[,"y2"]),col="green", lwd = 2, lty = 1)

Ghayabh/predictive-microbiology documentation built on Nov. 14, 2020, 7:54 p.m.