# Properly changing the time scale of a parameter in a growth model

I have a two-population model, where one of the populations is a bacterial culture with its growth described as a logistic growth, with a reported growth rate of $2 \log\hbox{bacteria hour}^{-1}$ and a death rate of $1.5 \log\hbox{bacteria hour}^{-1}$ and a carrying capacity of $7 \log\hbox{bacteria}$. However, my model studies the interaction between bacteria and fungi in a time scale of days, but if I try to directly rescale these parameters, I get a growth rate of $48 \log\hbox{bacteria day}^{-1}$ and a death rate of $36 \log\hbox{bacteria day}^{-1}$, which is absurd, given the carrying capacity of bacteria.

Is there a standard method for properly rescaling these parameters for bacterial growth, without having to change the model? What alternatives do I have?

## 1 Answer

These values are not absurd: it's just a different unit, it does not change the reality of th phenomenon.

The fact that your population can grow by a $48$ or $36~\mathrm{log}$ factor in one day, while the carrying capacity is $10^7$ bacteria, only means that the growth happens in less than one day (once the latency phase is over). Many bacterial population can grow in less than one day, it is not shocking.

In my opinion, it is not absurd to use the growth rates in $\mathrm{log}~ \textrm{bacteria} \cdot \textrm{day}^{-1}$. There is not need to rescale values if you just want to convert hours into days.

• My issue is that when performing simulations day-by-day the model is doing huge jumps each day, which the carrying capacity is unable to sustain. Would in that case perform jumps hour by hour be better? – Rono Aug 3 '17 at 14:21
• It appears to me that a day-by-day study is not in line with the time scale at which bacterial growth occurs. Bacterial growth is generally studied hour-by-hour, or even min-by-min – Flo Aug 3 '17 at 14:25