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Related Concept Videos

Multicompartment Models: Overview01:14

Multicompartment Models: Overview

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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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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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Mechanistic Models: Overview of Compartment Models01:21

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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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Clearance measures drug elimination from the central compartment, including plasma and highly perfused organs like kidneys and liver. Its calculation varies depending on pharmacokinetic models and administration routes. The one-compartment model, for instance, portrays the pharmacokinetics of polar drugs such as aminoglycoside antibiotics administered intravenously and readily excreted in urine. In this case, clearance is influenced by the terminal rate constant (λz) and the total volume...
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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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Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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Continuous and discrete SIR-models with spatial distributions.

Seong-Hun Paeng1, Jonggul Lee2

  • 1Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul, 143-701, Korea. shpaeng@konkuk.ac.kr.

Journal of Mathematical Biology
|November 1, 2016
PubMed
Summary

This study introduces spatial SIR-models using an infectious radius, not individual dispersion, to simulate disease spread. Simulation results show epidemic speed and size are influenced by population density and infectious radius.

Keywords:
Infectious radiusSIR-modelSpatial distribution

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Computational Science

Background:

  • The standard SIR (Susceptible-Infected-Removed) model lacks spatial dynamics.
  • Existing spatial models often rely on individual dispersion assumptions, which are unrealistic for human populations.
  • Disease transmission occurs even without significant individual movement.

Purpose of the Study:

  • To propose novel continuous and discrete SIR-models incorporating spatial distributions.
  • To investigate the impact of an infectious radius on disease propagation.
  • To analyze how population density and infectious radius affect epidemic dynamics.

Main Methods:

  • Development of continuous and discrete SIR-models that account for spatial factors.
  • Simulation of disease spread using the proposed models.
  • Analysis of simulation outputs to determine relationships between parameters and epidemic characteristics.

Main Results:

  • The proposed models successfully demonstrate spatial disease distribution.
  • Epidemic propagation speed is shown to be dependent on population density and infectious radius.
  • The overall size of an epidemic is also influenced by population density and infectious radius.

Conclusions:

  • Spatial SIR-models utilizing an infectious radius offer a more realistic approach to simulating human epidemics.
  • Population density and infectious radius are critical factors determining epidemic spread and magnitude.
  • These findings can inform public health strategies for disease containment.