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 Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

57
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...
57
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

450
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
450
Life Histories01:29

Life Histories

18.0K
Overview
18.0K
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

527
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...
527
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

44
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...
44
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

84
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
84

You might also read

Related Articles

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

Sort by
Same author

Towards a classification framework for patient safety incidents and adverse events for a mental health community-based model of service provision.

Revista de psiquiatria y salud mental·2022
Same author

Collocation of Next-Generation Operators for Computing the Basic Reproduction Number of Structured Populations.

Journal of scientific computing·2020
Same author

Efficient numerical computation of the basic reproduction number for structured populations.

Journal of computational and applied mathematics·2020
Same author

On the Reproduction Number of a Gut Microbiota Model.

Bulletin of mathematical biology·2017
Same author

New surgical approach to advanced Kienböck disease: lunate replacement with pedicled vascularized scaphoid graft and radioscaphoidal partial arthrodesis.

Techniques in hand & upper extremity surgery·2013
Same author

Outbreak analysis of an SIS epidemic model with rewiring.

Journal of mathematical biology·2012

Related Experiment Video

Updated: Jul 11, 2025

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

8.8K

Numerical approach to an age-structured Lotka-Volterra model.

Jordi Ripoll1, Jordi Font1

  • 1Department of Computer Science, Applied Mathematics and Statistics, University of Girona, Campus Montilivi, 17003 Girona, Spain.

Mathematical Biosciences and Engineering : MBE
|November 3, 2023
PubMed
Summary

This study explores age-dependent interactions in predator-prey models using partial differential equations and renewal equations. It reveals how age affects population dynamics, leading to stable limit cycles and complex behaviors like Hopf bifurcations.

Keywords:
Hopf bifurcationStructured ecological modelschronological ageefficient numerical methodspredator-prey modelsrenewal equations

More Related Videos

Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System
09:23

Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System

Published on: November 1, 2017

11.9K
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

3.4K

Related Experiment Videos

Last Updated: Jul 11, 2025

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

8.8K
Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System
09:23

Methodology for Developing Life Tables for Sessile Insects in the Field Using the Whitefly, Bemisia tabaci, in Cotton As a Model System

Published on: November 1, 2017

11.9K
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

3.4K

Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Ecological Modeling

Background:

  • Predator-prey models are crucial for understanding ecological interactions.
  • Age structure can significantly influence population dynamics and stability.
  • Previous models often simplified or ignored age-dependent effects.

Purpose of the Study:

  • To investigate the impact of age-dependent interactions in a structured predator-prey model.
  • To compare the efficacy of partial differential equation (PDE) and renewal equation approaches.
  • To analyze the stability and time-evolution of interacting populations.

Main Methods:

  • Development of efficient numerical methods for stability analysis.
  • Computation of population time-evolution, including oscillating orbits.
  • Analysis of asymptotic behavior using age-profiles and ordinary differential equation (ODE) limit systems.

Main Results:

  • Demonstrated age-dependent interactions leading to Hopf bifurcations.
  • Observed transitions from stable coexistence equilibria to periodic orbits and stable limit cycles.
  • Characterized asymptotic behavior for age-independent interactions.

Conclusions:

  • Age structure plays a critical role in predator-prey dynamics, influencing stability and leading to complex behaviors.
  • The PDE and renewal equation approaches offer complementary insights.
  • Numerical methods developed are accurate for analyzing population dynamics.