Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

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...

Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

Exponential Equations with Logarithms: Problem Solving

Exponential Equations with Logarithms: Problem Solving

In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...

Steps in Outbreak Investigation

Steps in Outbreak Investigation

In the ever-evolving field of public health, statistical analysis serves as a cornerstone for understanding and managing disease outbreaks. By leveraging various statistical tools, health professionals can predict potential outbreaks, analyze ongoing situations, and devise effective responses to mitigate impact. For that to happen, there are a few possible stages of the analysis:

Exponential Functions with Base e

Exponential Functions with Base e

Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...

Generation Time

Generation Time

Bacterial generation time, the period required for a bacterial population to double during its exponential growth phase, serves as a critical measure of microbial growth dynamics under optimal conditions. This parameter varies significantly across bacterial species and can be influenced by factors such as temperature, pH, and the availability of nutrients. For example, Escherichia coli can achieve a generation time of approximately 20 minutes, while Mycobacterium tuberculosis exhibits a much...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Impact of red blood cell transfusion and transfusion strategies on clinical outcomes in extremely low gestational age neonates.

Frontiers in pediatrics·2026

Same author

Time evolution of infection state correlation of nodes in an SIR model on a random contact network.

Mathematical biosciences·2026

Same author

Integrating Transcriptomics and Gut Microbiota Analysis Reveals Adaptive Mechanisms of Alkaline Stress on the Molting and Intestinal Immune Responses in Pacific White Shrimp, <i>Litopenaeus vannamei</i>.

Life (Basel, Switzerland)·2026

Same author

Mechanistic modelling of highly pathogenic avian influenza: A scoping review revealing critical gaps in cross-species transmission models.

PloS one·2026

Same author

Retrospective analysis of age-specific non-pharmaceutical interventions on wild-type SARS-CoV-2 in Canada.

BMC public health·2026

Same author

Unraveling the phototransformation of 2,4,6-tribromophenol: Aqueous mechanisms involving ·OH and the emergence of hydroxylated PBDEs.

Water research·2026

Search research articles

Related Experiment Video

Updated: Dec 30, 2025

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

Estimating epidemic exponential growth rate and basic reproduction number.

¹Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.

Infectious Disease Modelling

|January 21, 2020

Summary

Estimating epidemic growth rates is challenging due to data limitations and decay over time. This study explores using maximum likelihood methods and simple models for accurate growth rate estimation in fast epidemics.

Keywords:

Epidemic curve Exponential growth rate Maximum likelihood estimation Phenomenological models

More Related Videos

Estimating Virus Production Rates in Aquatic Systems

Estimating Virus Production Rates in Aquatic Systems

Published on: September 22, 2010

Pairwise Growth Competition Assay for Determining the Replication Fitness of Human Immunodeficiency Viruses

Pairwise Growth Competition Assay for Determining the Replication Fitness of Human Immunodeficiency Viruses

Published on: May 4, 2015

Related Experiment Videos

Last Updated: Dec 30, 2025

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Saccharomyces cerevisiae Exponential Growth Kinetics in Batch Culture to Analyze Respiratory and Fermentative Metabolism

Published on: September 30, 2018

Estimating Virus Production Rates in Aquatic Systems

Estimating Virus Production Rates in Aquatic Systems

Published on: September 22, 2010

Pairwise Growth Competition Assay for Determining the Replication Fitness of Human Immunodeficiency Viruses

Pairwise Growth Competition Assay for Determining the Replication Fitness of Human Immunodeficiency Viruses

Published on: May 4, 2015

Area of Science:

Epidemiology
Mathematical Modeling

Background:

The initial exponential growth rate is crucial for assessing epidemic severity and relates to the basic reproduction number.
Estimating this growth rate from epidemic curves presents challenges due to temporal decay and limited data points, especially in fast-spreading epidemics.

Purpose of the Study:

To discuss and evaluate methods for estimating the initial exponential growth rate of epidemics.
To address the challenges of over-fitting and model selection in fast epidemic scenarios.

Main Methods:

Utilizing the maximum likelihood method for growth rate estimation.
Employing simple mathematical models to represent epidemic curves.

Main Results:

The study discusses the application of maximum likelihood estimation for epidemic growth rates.
Analysis focuses on overcoming limitations posed by sparse data in fast epidemics.

Conclusions:

Maximum likelihood estimation with simple models offers a viable approach for estimating epidemic growth rates.
Accurate estimation is vital for understanding epidemic dynamics and informing public health interventions.