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

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

125
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,...
125
Pole and System Stability01:24

Pole and System Stability

422
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
422
Stability01:28

Stability

188
The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
188
Nonlinear Pharmacokinetics: Causes of Nonlinearity01:22

Nonlinear Pharmacokinetics: Causes of Nonlinearity

341
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
341
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

135
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
135
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

521
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
521

You might also read

Related Articles

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

Sort by
Same author

Diagnostic performance of RIPASA versus modified Alvarado score in acute appendicitis: a prospective diagnostic accuracy study from a tertiary centre in India.

BMC surgery·2026
Same author

An explainable multi-stage framework for brain tumor classification using hybrid feature fusion and EfficientNetB5 model.

Scientific reports·2026
Same author

Activity of Didesmethylrocaglamide in High Grade Serous Ovarian Cancer Using Preclinical In Vitro and In Vivo Models.

Journal of natural products·2026
Same author

Fractional-order epidemic modeling with a deep neural network framework.

Scientific reports·2026
Same author

Recent Advances in Bipolar Membrane Engineering for Direct Seawater Electrolysis: Improved Efficiency and Stability for Hydrogen Generation.

Small (Weinheim an der Bergstrasse, Germany)·2025
Same author

Nanomaterial interventions for wound healing: Current status of preclinical and clinical studies.

Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society·2025
Same journal

The Safety and Efficacy of Cardiac Stem Cell Therapy for Cardiovascular Disease: A Meta-Analysis of Randomized Controlled Trials.

Critical reviews in biomedical engineering·2026
Same journal

Local-Global-Graph Network-Based Biokey Generation with Electrocardiogram Signal and Lightweight Authentication in Cloud-Based Internet of Medical Things Networks.

Critical reviews in biomedical engineering·2026
Same journal

Diffusion Tensor Imaging for Brain Injury Assessment: Methodological Foundations and Clinical Insights.

Critical reviews in biomedical engineering·2026
Same journal

Novel Investigation of Hepatitis B Transmission Dynamics via Fractal-Fractional Operators of Variable and Constant Order with Memory Effects.

Critical reviews in biomedical engineering·2026
Same journal

An Improved YOLOv8-Based Object Detection Algorithm for Skin Diseases.

Critical reviews in biomedical engineering·2026
Same journal

A Numerical Comparison of Magnetic Nanoparticle Hyperthermia in Breast, Muscle, and Prostate Tumors.

Critical reviews in biomedical engineering·2025
See all related articles

Related Experiment Video

Updated: Sep 13, 2025

Software for Analysis of Heart Rate and Blood Pressure Time-series Data from the Valsalva Maneuver
14:28

Software for Analysis of Heart Rate and Blood Pressure Time-series Data from the Valsalva Maneuver

Published on: June 27, 2025

432

Nonlinear Dynamics and Stability Analysis of a Pandemic Model Using Homotopy Perturbation.

Garima Agarwal1, Man Mohan Singh1, Rashid Jan2

  • 1Department of Mathematics and Statistics, School of Physical and Biological Sciences, Manipal University Jaipur, India.

Critical Reviews in Biomedical Engineering
|August 1, 2025
PubMed
Summary
This summary is machine-generated.

This study numerically solves SEIR models using the homotopy perturbation method. It explores fractional and integer orders, analyzing population dynamics and stability for susceptible, exposed, infected, and recovered individuals.

More Related Videos

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

2.3K
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

Related Experiment Videos

Last Updated: Sep 13, 2025

Software for Analysis of Heart Rate and Blood Pressure Time-series Data from the Valsalva Maneuver
14:28

Software for Analysis of Heart Rate and Blood Pressure Time-series Data from the Valsalva Maneuver

Published on: June 27, 2025

432
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

2.3K
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

Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Nonlinear Dynamics

Background:

  • Compartmental models like SEIR are crucial for understanding disease spread.
  • Nonlinear mathematical models often require advanced numerical techniques for solutions.
  • Fractional calculus offers a more nuanced approach to modeling dynamic systems.

Purpose of the Study:

  • To provide a numerical solution for Susceptible, Exposed, Infected, and Recovered (SEIR) models.
  • To analyze population dynamics across different orders (fractional and integer).
  • To investigate the impact of parameters alpha and beta on SEIR population categories.

Main Methods:

  • Application of the homotopy perturbation method for solving nonlinear SEIR models.
  • Graphical analysis of population dynamics for susceptible, exposed, infected, and recovered individuals.
  • Exploration of both fractional and integer order models.

Main Results:

  • The homotopy perturbation method successfully provided numerical solutions for SEIR models.
  • Graphical representations illustrated the behavior of different population categories under varying parameters.
  • Stability analysis was performed and visualized within the population graphs.

Conclusions:

  • The homotopy perturbation method is effective for solving nonlinear SEIR models.
  • Fractional order models offer potential for more detailed epidemic analysis.
  • Parameter variations significantly influence population dynamics and model stability.