基于实验性混合批培养的Escherichia coli和Lactobacillus acidophilus生长的数学建模

The bacterial growth curve is a fundamental concept in microbiology that describes the dynamics of bacterial population growth in a closed system with controlled environmental conditions, such as temperature and nutrient availability. This curve is divided into four distinct phases: lag, log (exponential), stationary, and death phases, each reflecting a unique stage of bacterial adaptation and growth. During the lag phase, bacteria acclimate to their surroundings by synthesizing essential...

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...

Estimating microbial growth is essential for understanding population dynamics and environmental adaptations. Indirect methods provide valuable insights by measuring parameters such as turbidity, metabolic activity, and biomass, enabling efficient and reproducible assessments.During exponential growth, microbial cells scatter light proportionally to their biomass, a principle used in turbidity measurements. About one million cells per milliliter produce detectable scattering, which a...