Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

117
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...
117
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

145
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
145
Model Approaches for Pharmacokinetic Data: Compartment Models01:14

Model Approaches for Pharmacokinetic Data: Compartment Models

299
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...
299
Three-Compartment Open Model01:06

Three-Compartment Open Model

576
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...
576
Two-Compartment Open Model: Extravascular Administration01:12

Two-Compartment Open Model: Extravascular Administration

435
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...
435
Compartment Models: Single-Compartment Model01:14

Compartment Models: Single-Compartment Model

2.7K
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...
2.7K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Fractional-calculus analysis of the transmission dynamics of the dengue infection.

Chaos (Woodbury, N.Y.)·2021
Same author

Numerical simulation and stability analysis for the fractional-order dynamics of COVID-19.

Results in physics·2021
Same author

Some new and modified fractional analysis of the time-fractional Drinfeld-Sokolov-Wilson system.

Chaos (Woodbury, N.Y.)·2020
Same author

Some new mathematical models of the fractional-order system of human immune against IAV infection.

Mathematical biosciences and engineering : MBE·2020
Same author

An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus.

Chaos, solitons, and fractals·2020
Same author

Representation of [Formula: see text]-Bernstein polynomials in terms of [Formula: see text]-Jacobi polynomials.

Journal of inequalities and applications·2017

Related Experiment Video

Updated: Oct 31, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K

Power-series solution of compartmental epidemiological models.

H M Srivastava1,2,3,4, I Area5, J J Nieto6

  • 1Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.

Mathematical Biosciences and Engineering : MBE
|July 2, 2021
PubMed
Summary

This study introduces power-series solutions as a novel method for solving complex epidemiological models like SIR and SAIRP. This approach offers an accurate alternative for analyzing disease dynamics, including during pandemics like COVID-19.

Keywords:
COVID-19compartmental epidemiological modelnumerical approximationpower-series solution

More Related Videos

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

2.3K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.5K

Related Experiment Videos

Last Updated: Oct 31, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

10.8K
An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

2.3K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.5K

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Compartmental epidemiological models are crucial for understanding disease spread.
  • Solving the nonlinear differential equations governing these models can be challenging.
  • Previous applications include analysis of the COVID-19 pandemic.

Purpose of the Study:

  • To present power-series solutions as an alternative method for solving compartmental epidemiological models.
  • To demonstrate the applicability of this methodology using SIR and SAIRP models.
  • To validate the accuracy of the proposed approach through numerical experiments.

Main Methods:

  • Utilizing power-series expansions to find solutions for systems of nonlinear differential equations.
  • Applying the methodology to a standard SIR (Susceptible-Infectious-Recovered) model.
  • Extending the analysis to a more complex SAIRP (Susceptible-Asymptomatic-Infectious-Recovered-Positive) model.

Main Results:

  • The power-series method provides accurate solutions for the considered epidemiological models.
  • The approach effectively handles the nonlinear dynamics inherent in disease transmission.
  • Numerical experiments confirm the reliability and precision of the power-series solutions.

Conclusions:

  • Power-series solutions offer a viable and accurate alternative for analyzing compartmental epidemiological models.
  • This methodology can be applied to various models, including those relevant to real-world pandemics.
  • The study validates a new computational tool for epidemiological research.