growthrates (version 0.8.4)

grow_huang: Growth Model According to Huang

Description

Huangs growth model written as analytical solution of the differential equations.

Usage

grow_huang(time, parms)

Value

vector of dependent variable (y).

Arguments

time

vector of time steps (independent variable).

parms

named parameter vector of Huang's growth model with:

• y0 initial value of abundance,

• mumax maximum growth rate (1/time),

• K carrying capacity (max. total concentration of cells),

• alpha shape parameter determining the curvature,

• lambda parameter determining the lag time.

Details

The version of the equation used in this package has the following form: $$B = time + 1/alpha * log((1+exp(-alpha * (time - lambda)))/(1 + exp(alpha * lambda)))$$ $$log(y) = log(y0) + log(K) - log(y0 + (K - y0) * exp(-mumax * B))$$

In contrast to the original publication, all parameters related to population abundance (y, y0, K) are given as untransformed values. They are not log-transformed.
In general, using log-transformed parameters would indeed be a good idea to avoid the need of constained optimization, but tests showed that box-constrained optimization worked resonably well. Therefore, handling of optionally log-transformed parameters was removed from the package to avoid confusion. If you want to discuss this, please let me know.

References

Huang, Lihan (2008) Growth kinetics of Listeria monocytogenes in broth and beef frankfurters - determination of lag phase duration and exponential growth rate under isothermal conditions. Journal of Food Science 73(5), E235 -- E242. tools:::Rd_expr_doi("10.1111/j.1750-3841.2008.00785.x")

Huang, Lihan (2011) A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new Belehdradek-type model for evaluating the effect of temperature on growth rate. Food Microbiology 28, 770 -- 776. tools:::Rd_expr_doi("10.1016/j.fm.2010.05.019")

Huang, Lihan (2013) Introduction to USDA Integrated Pathogen Modeling Program (IPMP). Residue Chemistry and Predictive Microbiology Research Unit. USDA Agricultural Research Service.

See Also

Other growth models: grow_baranyi(), grow_exponential(), grow_gompertz2(), grow_gompertz(), grow_logistic(), grow_richards(), growthmodel, ode_genlogistic(), ode_twostep()

Examples

time <- seq(0, 30, length=200)
y    <- grow_huang(time, c(y0=0.01, mumax=.1, K=0.1, alpha=1.5, lambda=3))[,"y"]
plot(time, y, type="l")
plot(time, y, type="l", log="y")