expandedjameson: This is an expanded version of the Jameson model by Giménez...

In Ghayabh/bacterial-growth: bacterialgrowth Package

Description

This is an expanded version of the Jameson model by Giménez and Dalgaard (2004),this new model includes a temperature dependent parameter (gamma).

Usage

expandedjameson(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{array}{l} t<t_{\operatorname{lag}-S}, \quad \frac{\mathrm{d} S / \mathrm{d} t}{S_{t}}=0 \\ t ≥q t_{\operatorname{lag}-S}, \quad \frac{\mathrm{d} S / \mathrm{d} t}{S_{t}}=μ_{\max }^{S} \times≤ft(1-\frac{S_{t}}{S_{\max }}\right) \times≤ft(1-\frac{γ \times \mathrm{NB}_{t}}{\mathrm{NB}_{\max }}\right) \\ t<t_{\mathrm{lag}-\mathrm{NB}}, \quad \frac{\mathrm{d} \mathrm{NB} / \mathrm{d} t}{\mathrm{NB}}=0 \\ t ≥q t_{\mathrm{lag}-\mathrm{NB}}, \quad \frac{\mathrm{d} \mathrm{NB} / \mathrm{dt}}{\mathrm{NB}}=μ_{\max }^{\mathrm{NB}} \times≤ft(1-\frac{\mathrm{NB}_{t}}{\mathrm{NB}_{\max }}\right) \times≤ft(1-\frac{S_{t}}{S_{\operatorname{mox}}}\right) \end{array}\end{equation}

Value

dQ1,dQ2,dy1,dy2

Examples

library(deSolve)
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 = expandedjameson,
parms = c(gamma=1, 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/bacterial-growth documentation built on Dec. 31, 2020, 12:04 p.m.