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

Steps in Outbreak Investigation01:18

Steps in Outbreak Investigation

249
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:
249
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

101
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...
101
Causality in Epidemiology01:21

Causality in Epidemiology

1.0K
Causality or causation is a fundamental concept in epidemiology, vital for understanding the relationships between various factors and health outcomes. Despite its importance, there's no single, universally accepted definition of causality within the discipline. Drawing from a systematic review, causality in epidemiology encompasses several definitions, including production, necessary and sufficient, sufficient-component, counterfactual, and probabilistic models. Each has its strengths and...
1.0K
Statistical Methods for Analyzing Epidemiological Data01:25

Statistical Methods for Analyzing Epidemiological Data

592
Epidemiological data primarily involves information on specific populations' occurrence, distribution, and determinants of health and diseases. This data is crucial for understanding disease patterns and impacts, aiding public health decision-making and disease prevention strategies. The analysis of epidemiological data employs various statistical methods to interpret health-related data effectively. Here are some commonly used methods:
592
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

115
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...
115
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

691
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...
691

You might also read

Related Articles

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

Sort by
Same author

<i>In vitro</i> dormancy models improve ability to predict treatment response in severe marmoset tuberculosis lesions.

bioRxiv : the preprint server for biology·2026
Same author

Distinct mechanisms drive post-antibiotic Tuberculosis relapse post-cure versus post-treatment-failure.

bioRxiv : the preprint server for biology·2026
Same author

Community-level wastewater surveillance with machine learning methods to assess underreporting of COVID-19 case counts.

mLife·2026
Same author

A novel machine-learning based optimization: identifying new treatment regimens for tuberculosis.

Numerical algebra, control and optimization·2025
Same author

Capturing the implications of residential segregation for the dynamics of infectious disease transmission.

Annals of epidemiology·2025
Same author

GEODE: an <i>in silico</i> tool that translates <i>in vitro</i> to <i>in vivo</i> predictions of tuberculosis antibiotic combination efficacy.

Frontiers in pharmacology·2025

Related Experiment Video

Updated: Oct 8, 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

Structural identifiability analysis of age-structured PDE epidemic models.

Marissa Renardy1, Denise Kirschner2, Marisa Eisenberg3,4

  • 1Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, USA. renardy@umich.edu.

Journal of Mathematical Biology
|January 4, 2022
PubMed
Summary

We developed a new method for analyzing the identifiability of age-structured partial differential equation (PDE) models. This framework helps determine how well model parameters can be estimated from data, crucial for reliable predictions.

Keywords:
Age structureEpidemiologyModelingPartial differential equationsTuberculosis

More Related Videos

Measurement of Lifespan in Drosophila melanogaster
10:00

Measurement of Lifespan in Drosophila melanogaster

Published on: January 7, 2013

34.7K
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 8, 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
Measurement of Lifespan in Drosophila melanogaster
10:00

Measurement of Lifespan in Drosophila melanogaster

Published on: January 7, 2013

34.7K
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:

  • Mathematical Biology
  • Computational Biology
  • Epidemiology

Background:

  • Model parameter estimation is vital for computational and mathematical models.
  • Identifiability analysis assesses parameter estimability from data, ensuring reliable predictions.
  • Structural identifiability of ordinary differential equation (ODE) models is well-established, but less so for age-structured partial differential equation (PDE) models.

Purpose of the Study:

  • To establish a pipeline for structural identifiability analysis of age-structured PDE models.
  • To derive identifiability results for specific age-structured models.
  • To demonstrate the framework using epidemic models and compare PDE with ODE systems.

Main Methods:

  • Utilized a differential algebra framework for structural identifiability analysis.
  • Applied the pipeline to age-structured PDE models, specifically a Susceptible-Exposed-Infected (SEI) epidemic model.
  • Compared identifiability results between PDE and corresponding ODE models and explored age-dependent parameter effects.

Main Results:

  • Successfully established a pipeline for structural identifiability analysis of age-structured PDE models.
  • Derived identifiability results for specific age-structured models, demonstrating the framework's utility.
  • Showcased the application of practical identifiability analysis within the developed framework.

Conclusions:

  • The differential algebra framework provides a robust method for analyzing the structural identifiability of age-structured PDE models.
  • The framework facilitates a deeper understanding of parameter estimability in complex biological systems.
  • This work bridges a gap in identifiability analysis for PDE models, with implications for various fields including epidemiology.