Huangs growth model written as analytical solution of the differential equations.
vector of time steps (independent variable).
named parameter vector of Huang's growth model with:
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.
vector of dependent variable (
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. 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. 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.
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