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Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
It is ideally spatially unstructured and temporally unstructured, in a steady state defined by the rates of nutrient supply and bacterial growth. In comparison to batch culture, bacteria are maintained in exponential growth phase, and the growth rate of the bacteria is known. Related devices include turbidostats and auxostats.
When calculating or discussing relative growth rate, it is important to pay attention to the units of time being considered. [2] For example, if an initial population of S 0 bacteria doubles every twenty minutes, then at time interval it is given by solving the equation:
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910–1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient.
Figure 1: A bi-phasic bacterial growth curve.. A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), individual body height or biomass (in physiology, for growth analysis of individuals).
Growth rates of 2 bacterial species will differ by unexpected orders of magnitude if the doubling times of the 2 species differ by even as little as 10 minutes. In eukaryotes such as animals, fungi, plants, and protists, doubling times are much longer than in bacteria. This reduces the growth rates of eukaryotes in comparison to Bacteria.
For example, if a contact network can be approximated with an Erdős–Rényi graph with a Poissonian degree distribution, and the disease spreading parameters are as defined in the example above, such that is the transmission rate per person and the disease has a mean infectious period of , then the basic reproduction number is = [22] [23 ...