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Related Concept Videos

The Thermodynamics of Mixing01:28

The Thermodynamics of Mixing

Mixing is a fascinating phenomenon in thermodynamics, particularly when considering the Gibbs energy of a mixture at constant temperature and pressure. This energy, denoted as G, tends to decrease during spontaneous mixing processes, offering insights into the composition changes that occur.Imagine two ideal gases, initially separated in different containers, with amounts nA and nB, respectively, both at a temperature T and pressure p. The chemical potentials of these gases have their 'pure'...
Pharmacodynamic Models: Additive and Proportional Drug Effect Model01:09

Pharmacodynamic Models: Additive and Proportional Drug Effect Model

Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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...
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model

Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...

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Related Experiment Video

Updated: Jun 25, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

A contact-network-based formulation of a preferential mixing model.

Istvan Z Kiss1, Péter L Simon, Rowland R Kao

  • 1Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9RF, UK. i.z.kiss@sussex.ac.uk

Bulletin of Mathematical Biology
|February 14, 2009
PubMed
Summary

This study introduces a simple differential equation model for infectious disease spread, accounting for varied contact numbers and mixing patterns. The model accurately reflects how assortative and disassortative mixing impact disease transmission dynamics.

Related Experiment Videos

Last Updated: Jun 25, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Infectious disease dynamics are significantly influenced by contact heterogeneity and mixing patterns.
  • Assortative mixing ('like attaches to like') and disassortative mixing ('opposites attract') affect disease spread and epidemic size.
  • Existing models for preferential mixing, particularly in sexually transmitted diseases (STDs), can be complex.

Purpose of the Study:

  • To derive a simplified differential equation model for infectious disease transmission based on contact networks.
  • To incorporate preferential mixing based on the number of contacts into the model.
  • To analyze the impact of various mixing patterns (assortative to disassortative) on epidemiological outcomes.

Main Methods:

  • Developed a contact-network-based differential equation model.
  • Incorporated preferential mixing dependent on the number of contacts.
  • Analyzed model behavior across a spectrum of mixing patterns.

Main Results:

  • The derived model shows good qualitative agreement with established preferential mixing models for STDs.
  • The model successfully captures the influence of heterogeneous contact numbers on disease transmission.
  • Analytical results were derived for a range of mixing patterns, from completely disassortative to completely assortative.

Conclusions:

  • A simple, adaptable differential equation model can effectively represent complex mixing patterns in disease transmission.
  • This model provides a tractable framework for understanding how contact heterogeneity and assortativity influence epidemic dynamics.
  • The findings have implications for predicting and controlling infectious diseases in populations with diverse contact structures.