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

Stability of structures01:14

Stability of structures

627
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
627
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

413
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...
413
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

1.2K
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
1.2K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

965
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
965
Population Growth00:57

Population Growth

29.6K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
29.6K
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

342
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...
342

You might also read

Related Articles

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

Sort by
Same author

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect.

Acta biotheoretica·2022
Same author

An age and space structured SIR model describing the Covid-19 pandemic.

Journal of mathematics in industry·2020
Same author

Special issue: Mathematical Modeling with Measures.

Mathematical biosciences and engineering : MBE·2020
Same author

Optimizing vaccination strategies in an age structured SIR model.

Mathematical biosciences and engineering : MBE·2020
Same author

A modeling framework for biological pest control.

Mathematical biosciences and engineering : MBE·2020
Same author

Preface to '' Modeling with measures ''.

Mathematical biosciences and engineering : MBE·2015
Same journal

Modeling the impact of budget limitation on the screening and treatment pathway of HPV-induced precancerous cervical lesions.

Mathematical biosciences and engineering : MBE·2026
Same journal

Modeling the effects of trait-mediated dispersal on coexistence of two species: Competition and non-consumptive predator-prey.

Mathematical biosciences and engineering : MBE·2026
Same journal

A close look at the viral reduction rate in target cell limited models.

Mathematical biosciences and engineering : MBE·2026
Same journal

A stochastic agent-based model for simulating tumor-immune dynamics and evaluating therapeutic strategies.

Mathematical biosciences and engineering : MBE·2026
Same journal

Addressing domain shift via imbalance-aware domain adaptation in embryo development assessment.

Mathematical biosciences and engineering : MBE·2026
Same journal

Effect of drug resistance on an HIV epidemic in heterogeneous populations.

Mathematical biosciences and engineering : MBE·2026
See all related articles

Related Experiment Video

Updated: Apr 15, 2026

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

9.3K

Stability and optimization in structured population models on graphs.

Rinaldo M Colombo1, Mauro Garavello

  • 1INdAM Unit, University of Brescia, Brescia, Italy. rinaldo.colombo@unibs.it.

Mathematical Biosciences and Engineering : MBE
|March 27, 2015
PubMed
Summary
This summary is machine-generated.

This study proves the existence and uniqueness of solutions for initial-boundary value problems in balance laws. The findings ensure stability for various biological and resource management models, guiding optimal control strategies.

More Related Videos

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K
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

2.7K

Related Experiment Videos

Last Updated: Apr 15, 2026

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

9.3K
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

1.4K
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

2.7K

Area of Science:

  • Mathematical modeling
  • Applied mathematics
  • Theoretical biology

Background:

  • Initial-boundary value problems for systems of balance laws are crucial in modeling complex phenomena.
  • Understanding solution behavior, including existence, uniqueness, and stability, is fundamental for reliable predictions.
  • Existing models often lack comprehensive analysis of stability with respect to boundary conditions.

Purpose of the Study:

  • To establish the existence and uniqueness of solutions for a class of initial-boundary value problems in balance laws.
  • To demonstrate continuous dependence on the initial datum.
  • To prove stability with respect to the boundary condition, enabling broader model applicability.

Main Methods:

  • Rigorous mathematical analysis of partial differential equations.
  • Development of a specific boundary condition framework.
  • Application of stability theory to systems of balance laws.

Main Results:

  • Existence and uniqueness of solutions are proven.
  • Continuous dependence on the initial datum is established.
  • Stability with respect to the boundary condition is demonstrated for a generalized class of problems.

Conclusions:

  • The established stability results are applicable to diverse models, including juvenile-adult population dynamics, optimal mating ratios, and biological resource management.
  • This work provides a theoretical foundation for tackling optimal management and control problems.
  • Sufficient conditions for the existence of optimal choices and controls are derived, enhancing decision-making in applied scenarios.