A Model of Microbial Growth and Decay in a Closed Habitat Based on Combined Fermi's and the Logistic Equations

Microbial growth in a closed system can be described by a model based on the continuous logistic equation on which a Fermi's term is superimposed. The first component of the combined model accounts for growth and the second for decay. It has the form: N(t)=Ns/{1+exp[kg(tcg-t)]}/ {1+exp[k1(t-tcl)]} orN(t)=N0+[Ns-N0]/ {1+exp[kg(tcg-t)]}/ {1+exp[k1(t-tcl)]} whereN(t) andN0, are the instantaneous and initial numbers of cells, or an equivalent population size or density measure, andNsthe medium's capacity;kandtcare rate constants and characteristic times with the subscript g or l signifying growth or decay, respectively. The model has the versatility to account for a short or long lag time, populations starting from a very small or substantial inoculum and asymmetric or symmetric growth curves with a broad or sharp peak. The model was tested with published experimental growth curves of bacteria and cell cultures grown under very different conditions and had a good fit in all the cases. Its parameters could be used for quantitative comparison between growth patterns and assessment of the relative overall role of growth-promoting and decay-causing agents that shape the growth curve. At least in principle, they can also be used to map the effects of factors such as temperature and pH algebraically or graphically.