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Related Concept Videos

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The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A...
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The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (Emax), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (Emax) or the effect at zero drug concentration,...
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Related Experiment Video

Updated: Mar 14, 2026

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Disease dynamics in a coupled cholera model linking within-host and between-host interactions.

Xueying Wang1, Jin Wang2

  • 1a Department of Mathematics , Washington State University , Pullman , WA , USA.

Journal of Biological Dynamics
|September 21, 2016
PubMed
Summary

This study introduces a new model for cholera dynamics, linking human infection to environmental spread. Findings reveal challenges in controlling cholera due to backward bifurcation, impacting epidemic prevention.

Keywords:
34D2037H2047H20Cholera coupled modelsbackward bifurcationfast-slow analysislocal and global stabilitytype reproduction numberwithin-host and between-host dynamics

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Dynamics

Background:

  • Cholera is a severe intestinal infection caused by Vibrio cholerae.
  • Understanding both within-host and between-host dynamics is crucial for disease control.
  • Existing models may not fully capture the complex interplay between individual infection and population-level transmission.

Purpose of the Study:

  • To develop a novel modelling framework for cholera dynamics.
  • To investigate the link between within-host Vibrio cholerae growth and between-host transmission.
  • To analyze the conditions leading to backward bifurcation in cholera epidemics.

Main Methods:

  • A mathematical modelling framework integrating within-host and between-host dynamics.
  • Fast-slow analysis utilizing different time scales within the model.
  • Bifurcation analysis to identify conditions for backward bifurcation.

Main Results:

  • The model successfully links within-host bacterial growth to environmental spread and human-to-human transmission.
  • Sufficient and necessary conditions for backward bifurcation in cholera epidemics were derived.
  • Backward bifurcation indicates a potential for unstable disease-free equilibria, complicating control efforts.

Conclusions:

  • The proposed modelling framework provides new insights into cholera transmission dynamics.
  • The identified backward bifurcation highlights significant challenges in cholera prevention and control strategies.
  • Further research may focus on refining control measures in light of these findings.