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Related Concept Videos

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
137
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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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
783
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

164
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
164
Pharmacokinetic Models: Overview01:20

Pharmacokinetic Models: Overview

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Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal...
1.3K
Model Approaches for Pharmacokinetic Data: Compartment Models01:14

Model Approaches for Pharmacokinetic Data: Compartment Models

240
Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
Two primary types of compartment models are recognized: mammillary and catenary. The more...
240

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Proposal of a population wide genome-based testing for Covid-19.

Scientific reports·2022
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Related Experiment Video

Updated: Oct 3, 2025

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
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Back to the Roots: A Discrete Kermack-McKendrick Model Adapted to Covid-19.

Matthias Kreck1, Erhard Scholz2

  • 1Mathematische Institute der Universitäten Bonn und Frankfurt, Universität Bonn, Bonn, Deutschland.

Bulletin of Mathematical Biology
|February 17, 2022
PubMed
Summary

The standard SIR model for Covid-19 analysis is a simplification. An adapted Kermack-McKendrick model, incorporating vaccination and testing, shows quarantine improvements can drastically reduce pandemic spread.

Keywords:
Discrete epidemiological modelKermack–McKendrick

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Public Health

Background:

  • The standard SIR model is frequently used for Covid-19 pandemic analysis.
  • This model is often applied as a "black box" without acknowledging its derivation as a special case of the 1927 Kermack-McKendrick theory.
  • A deeper understanding of the underlying theory is crucial for accurate pandemic modeling.

Purpose of the Study:

  • To explain the Kermack-McKendrick theory and adapt it into a discrete model for Covid-19 analysis.
  • To incorporate crucial real-world factors like vaccination, mass testing, and viral mutants into the model.
  • To demonstrate the practical application and implications of this adapted model using German pandemic data.

Main Methods:

  • The study begins by detailing the foundational Kermack-McKendrick theory.
  • A discrete approach is employed to adapt the theory for computational analysis.
  • Medical data and specific parameters for vaccination, mass testing, and mutants are integrated to form the adapted K-McK-model.

Main Results:

  • The adapted K-McK-model was applied to analyze the Covid-19 pandemic's development in Germany.
  • The model's simulations revealed significant potential impacts of public health interventions.
  • A key finding indicates that a minor intervention, such as reducing quarantine time by one day, could lead to substantial improvements in pandemic control.

Conclusions:

  • The Kermack-McKendrick theory provides a more robust framework for Covid-19 modeling than the standard SIR model.
  • The adapted K-McK-model, by including vaccination, testing, and mutants, offers a more nuanced and realistic approach to pandemic analysis.
  • Even small adjustments in intervention strategies, like shortening quarantine periods, can have a profound positive effect on mitigating pandemic spread.