ode_twostep | R Documentation |
System of two differential equations describing bacterial growth as two-step process of activation (or adaptation) and growth.
ode_twostep(time, y, parms, ...) grow_twostep(time, parms, ...)
time |
actual time (for the ode) resp. vector of simulation time steps. |
y |
named vector with state of the system (yi, ya: abundance of inactive and active organisms, e.g. concentration of inactive resp. active cells). |
parms |
parameters of the two-step growth model:
|
... |
placeholder for additional parameters (for user-extended versions of this function) |
The model is given as a system of two differential equations:
dy_i/dt = -kw * yi
dy_a/dt = kw * yi + mumax * (1 - (yi + ya)/K) * ya
that are then numerically integrated ('simulated') according to time (t). The model assumes that the population consists of active (y_a) and inactive (y_i) cells so that the observed abundance is (y = y_i + y_a). Adapting inactive cells change to the active state with a first order 'wakeup' rate (kw).
Function ode_twostep
is the system of differential equations,
whereas grow_twostep
runs a numerical simulation over time.
A similar two-compartment model, but without the logistic term, was discussed by Baranyi (1998).
For ode_twostep
: matrix containing the simulation outputs.
The return value of has also class deSolve
.
For grow_twostep
: vector of dependent variable (y
):
time
time of the simulation
yi
concentration of inactive cells
ya
concentration of active cells
y
total cell concentration
Baranyi, J. (1998). Comparison of stochastic and deterministic concepts of bacterial lag. J. heor. Biol. 192, 403–408.
Other growth models:
grow_baranyi()
,
grow_exponential()
,
grow_gompertz2()
,
grow_gompertz()
,
grow_huang()
,
grow_logistic()
,
grow_richards()
,
growthmodel
,
ode_genlogistic()
Other growth models:
grow_baranyi()
,
grow_exponential()
,
grow_gompertz2()
,
grow_gompertz()
,
grow_huang()
,
grow_logistic()
,
grow_richards()
,
growthmodel
,
ode_genlogistic()
time <- seq(0, 30, length=200) parms <- c(kw = 0.1, mumax=0.2, K=0.1) y0 <- c(yi=0.01, ya=0.0) out <- ode(y0, time, ode_twostep, parms) plot(out) o <- grow_twostep(0:100, c(yi=0.01, ya=0.0, kw = 0.1, mumax=0.2, K=0.1)) plot(o)
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