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Related Concept Videos

Cholera01:25

Cholera

Cholera is an acute gastrointestinal disease caused by the Gram-negative bacterium Vibrio cholerae. It is transmitted primarily via the fecal-oral route through the ingestion of contaminated water or food.Vibrio cholerae is a motile, Gram-negative bacterium of the family Vibrionaceae, primarily associated with waterborne outbreaks in areas with inadequate sanitation. Although over 200 serogroups of V. cholerae exist, only O1 and O139 are responsible for epidemic cholera. The O1 serogroup,...
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Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Exponential Equations for Modeling Growth01:26

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 the relative...
Steps in Outbreak Investigation01:18

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Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Related Experiment Video

Updated: Jun 2, 2026

Laboratory Techniques Used to Maintain and Differentiate Biotypes of Vibrio cholerae Clinical and Environmental Isolates
07:58

Laboratory Techniques Used to Maintain and Differentiate Biotypes of Vibrio cholerae Clinical and Environmental Isolates

Published on: May 30, 2017

Global stability for cholera epidemic models.

Jianjun Paul Tian1, Jin Wang

  • 1Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA. jptian@math.wm.edu

Mathematical Biosciences
|April 26, 2011
PubMed
Summary
This summary is machine-generated.

This study analyzes mathematical models of cholera transmission, revealing complex dynamics between human populations and Vibrio cholerae bacteria. The findings enhance understanding of cholera

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Last Updated: Jun 2, 2026

Laboratory Techniques Used to Maintain and Differentiate Biotypes of Vibrio cholerae Clinical and Environmental Isolates
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Vibrio cholerae: Model Organism to Study Bacterial Pathogenesis - Interview
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Vibrio cholerae: Model Organism to Study Bacterial Pathogenesis - Interview

Published on: May 28, 2007

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Dynamics

Background:

  • Cholera is a water/food-borne disease caused by Vibrio cholerae.
  • Disease dynamics are complex due to multiple transmission routes and pathogen ecology.
  • Existing models and studies offer insights but incomplete understanding of cholera mechanisms persists.

Purpose of the Study:

  • To conduct global stability analysis for deterministic cholera epidemic models.
  • To investigate endemic global stability for biologically significant scenarios.
  • To deepen the fundamental understanding of cholera dynamics.

Main Methods:

  • Developed four-dimensional non-linear autonomous systems modeling human and V. cholerae populations.
  • Applied monotone dynamical systems, geometric approach, and Lyapunov functions.
  • Utilized techniques suitable for systems where Poincaré-Bendixson theory is inapplicable.

Main Results:

  • Achieved global stability analysis for several cholera epidemic models.
  • Investigated endemic stability across various biologically relevant cases.
  • Provided analytical tools for understanding complex cholera transmission.

Conclusions:

  • The analysis offers building blocks for comprehensive cholera studies.
  • Enhanced understanding of the fundamental mechanisms driving cholera dynamics.
  • Mathematical modeling provides crucial insights into infectious disease epidemiology.