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Related Concept Videos

Compartment Models: Single-Compartment Model01:14

Compartment Models: Single-Compartment Model

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The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...
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Compartment Models: Two-Compartment Model01:20

Compartment Models: Two-Compartment Model

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The two-compartment model divides the body into central and peripheral compartments to account for varying blood perfusion rates among organs and tissues, affecting drug distribution. The central compartment includes blood and highly perfused tissues with rapid drug distribution, while the peripheral compartment contains tissues with slower drug distribution. After a single IV bolus dose, the drug concentration is high in plasma and low in tissues. The drug distribution between compartments...
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Three-Compartment Open Model01:06

Three-Compartment Open Model

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The three-compartment open model is a pharmacokinetic model used to describe the distribution and elimination of drugs following extravascular administration. It comprises a central compartment representing the plasma and two peripheral compartments. The highly perfused peripheral compartment represents organs and tissues with a rich blood supply, such as the liver, kidneys, and lungs. The scarcely perfused peripheral compartment represents tissues with lower blood supply, such as adipose...
789
Two-Compartment Open Model: Extravascular Administration01:12

Two-Compartment Open Model: Extravascular Administration

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The two-compartment model for extravascular administration represents a drug's absorption and distribution process. It features a central compartment, where the drug is first absorbed, and a peripheral compartment, which illustrates the drug's distribution throughout the body. The rate of change in drug concentration in the central compartment is calculated by three exponents: absorption, distribution, and elimination.
The absorption exponent (ka) indicates the speed at which the drug...
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Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

307
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
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Related Experiment Video

Updated: Jan 3, 2026

Three Laboratory Procedures for Assessing Different Manifestations of Impulsivity in Rats
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Basic reproduction ratios for periodic and time-delayed compartmental models with impulses.

Zhenguo Bai1, Xiao-Qiang Zhao2

  • 1School of Mathematics and Statistics, Xidian University, Xi'an, 710071, China. zgbai@xidian.edu.cn.

Journal of Mathematical Biology
|November 27, 2019
PubMed
Summary

This study develops the theory of the basic reproduction number for impulsive, time-delayed models. Findings suggest the basic reproduction number may overestimate virus spread risk in averaged delayed impulsive systems.

Keywords:
Basic reproduction ratioComputer virusImpulsive modelsThreshold dynamicsTime delay

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Area of Science:

  • Mathematical epidemiology
  • Dynamical systems theory
  • Impulsive differential equations

Background:

  • The basic reproduction number (R0) is crucial for analyzing infectious disease dynamics.
  • Existing R0 theory is limited for periodic and time-delayed impulsive models.
  • Impulsive models are relevant for interventions like vaccination or treatment.

Purpose of the Study:

  • To extend the theory of the basic reproduction number (R0) to impulsive, time-delayed models.
  • To establish R0 as a threshold parameter for the stability of associated linear systems.
  • To analyze the global dynamics of a time-delayed computer virus model with impulse treatment.

Main Methods:

  • Development of R0 theory for a class of impulsive differential equations.
  • Analysis of the stability of the zero solution for a linearized impulsive system.
  • Application of the developed R0 theory to a specific computer virus model with time delays and impulse control.

Main Results:

  • Introduced a novel definition and framework for R0 in impulsive, time-delayed systems.
  • Demonstrated that the new R0 is a critical threshold parameter for system stability.
  • Derived a threshold criterion for the global dynamics of the computer virus model based on R0.

Conclusions:

  • The developed R0 theory provides a robust tool for analyzing complex epidemiological models.
  • The basic reproduction number for time-averaged delayed impulsive systems may overestimate virus spread risk.
  • Further research is needed to refine R0 calculations for time-delayed, impulsive systems.