Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Application of Integration: Problem Solving

Application of Integration: Problem Solving

The process of breathing involves the periodic intake and expulsion of air, known as the respiratory cycle, which typically lasts about five seconds. Modeling the volume of air inhaled into the lungs as a function of time provides insight into both the dynamics and efficiency of pulmonary ventilation. This volume is determined by integrating the airflow rate over time, which captures the cumulative effect of air entering the lungs.Sinusoidal Model of AirflowAirflow during respiration is not...

Steps in Outbreak Investigation

Steps in Outbreak Investigation

In the ever-evolving field of public health, statistical analysis serves as a cornerstone for understanding and managing disease outbreaks. By leveraging various statistical tools, health professionals can predict potential outbreaks, analyze ongoing situations, and devise effective responses to mitigate impact. For that to happen, there are a few possible stages of the analysis:

Regulation of Bacterial Virulence

Regulation of Bacterial Virulence

Pathogenic bacteria employ a range of regulatory mechanisms to modulate the expression of virulence genes in response to environmental and host-derived signals. These mechanisms ensure that virulence factors are expressed only under favorable conditions, thereby optimizing infection and survival strategies.Mechanisms of Virulence RegulationKey regulatory strategies include:Two-Component Systems: These consist of a membrane-bound sensor kinase and a cytoplasmic response regulator. Environmental...

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...

You might also read

Related Articles

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

Sort by

Same author

Comprehensive Characterization of the Odor-Active Compounds in Different Processed Varieties of Yunnan White Tea (<i>Camellia sinensis</i>) by GC×GC-O-MS and Chemometrics.

Foods (Basel, Switzerland)·2025

Same author

Xylooligosaccharides: A comprehensive review of production, purification, characterization, and quantification.

Food research international (Ottawa, Ont.)·2025

Same author

Correction: Unveiling the obstacles encountered by women doctors in the Pakistani healthcare system: A qualitative investigation.

PloS one·2025

Same author

TargetCLP: clathrin proteins prediction combining transformed and evolutionary scale modeling-based multi-view features via weighted feature integration approach.

Briefings in bioinformatics·2025

Same author

Systematic Review of Vaccine Strategies Against Tritrichomonas foetus Infection in Cattle: Insights, Challenges, and Prospects.

Parasite immunology·2025

Same author

Citrus diseases detection using innovative deep learning approach and Hybrid Meta-Heuristic.

PloS one·2025

Search research articles

Related Experiment Video

Updated: Jun 11, 2026

Evaluation of Host-Pathogen Responses and Vaccine Efficacy in Mice

Evaluation of Host-Pathogen Responses and Vaccine Efficacy in Mice

Published on: February 22, 2019

A time-delayed mathematical framework for analyzing pertussis transmission dynamics.

Ali Raza^1,2, Marek Lampart³, Eugenio M Rocha⁴

¹IT4Innovations, VSB-Technical University of Ostrava, 17 listopadu 2172/15, Ostrava, 708 33, Czech Republic. alimustasamcheema@gmail.com.

Scientific Reports

|June 9, 2026

Summary

Pertussis (whooping cough) outbreaks persist due to waning immunity and delayed responses. Mathematical modeling shows that incorporating time delays into vaccination strategies can reduce pertussis prevalence and aid eradication efforts.

Keywords:

Delay differential equations Delayed modeling Numerical results Pertussis dynamics Stability analysis Time delay effects

More Related Videos

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

Published on: September 28, 2022

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Related Experiment Videos

Last Updated: Jun 11, 2026

Evaluation of Host-Pathogen Responses and Vaccine Efficacy in Mice

Evaluation of Host-Pathogen Responses and Vaccine Efficacy in Mice

Published on: February 22, 2019

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness

Published on: September 28, 2022

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Epidemiology
Mathematical Biology
Public Health

Background:

Pertussis (whooping cough) remains a significant global public health concern, with increasing case numbers reported.
Classical epidemiological models often overlook the impact of time delays, such as waning immunity and behavioral responses, on disease dynamics.

Purpose of the Study:

To investigate the role of time delays in pertussis transmission dynamics.
To analyze the epidemiological impact of vaccination, waning immunity, and delayed behavioral responses using a deterministic modeling framework.

Main Methods:

Development of a deterministic, time-delayed compartmental model for pertussis transmission.
Analysis of model properties, equilibria, and stability using Routh-Hurwitz criterion and Lyapunov techniques.
Numerical simulations to explore subpopulation dynamics under various scenarios.

Main Results:

The basic reproduction number dictates the transition between pertussis elimination and persistence.
Time delays significantly influence epidemic patterns, leading to oscillations or damping.
Incorporating delays with vaccination strategies can reduce infection prevalence and promote disease eradication.

Conclusions:

Time-delayed mathematical models offer crucial insights into pertussis transmission dynamics.
Vaccination, waning immunity, and behavioral response delays interact to shape epidemic persistence.
The findings provide a mathematical foundation for enhancing public health strategies against pertussis.