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

Modeling with Differential Equations01:25

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...
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
Exponential Equations for Modeling Growth01:26

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...
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs01:21

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
Pharmacokinetic Models: Overview01:20

Pharmacokinetic Models: Overview

Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...

You might also read

Related Articles

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

Sort by
Same author

Effectiveness of pharmacological treatment in the secondary prevention of fragility fractures: A region-wide study.

Revista espanola de geriatria y gerontologia·2026
Same author

Health-economic challenges for new Alzheimer's disease treatments.

The journal of prevention of Alzheimer's disease·2026
Same author

Electronic health records reveals resilience patterns of cardiovascular disease in Basque centenarians.

Frontiers in aging·2026
Same author

Evaluation of the effectiveness of a screening program as compared to usual care in identifying patients with post-partum depression: a cohort study of 20,448 births in Bizkaia (Spain).

Journal of affective disorders·2026
Same author

Cost analysis of a virtual retina clinic versus fully face-to-face clinics.

Archivos de la Sociedad Espanola de Oftalmologia·2026
Same author

Hospitalization and referral for mental illness among people under 30 in Euskadi: a retrospective population-based cohort.

Gaceta sanitaria·2026

Related Experiment Video

Updated: Jun 20, 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

[Mathematical models for economic evaluation: dynamic models based on differential equations].

Roberto Pradas Velasco1, Fernando Antoñanzas Villar, Javier Mar

  • 1Universidad de La Rioja, Logroño, La Rioja, Spain. roberto.pradas@unirioja.es

Gaceta Sanitaria
|September 1, 2009
PubMed
Summary

This study combines decision trees and epidemiological models to evaluate the economic impact of infectious disease interventions, like influenza vaccination, by analyzing disease dynamics and healthcare costs.

Related Experiment Videos

Last Updated: Jun 20, 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

Area of Science:

  • Epidemiology
  • Health Economics
  • Mathematical Modeling

Context:

  • Evaluating preventative interventions for infectious diseases requires integrating disease dynamics with economic factors.
  • Traditional methods may not fully capture the complex interplay between disease progression and healthcare resource utilization.

Purpose:

  • To present a hybrid modeling approach combining decision trees and differential equation-based epidemiological models.
  • To assess the economic implications and epidemiologic impact of influenza vaccination in Spain.

Summary:

  • A dynamic system of differential equations was adapted to model influenza epidemic behavior in Spain.
  • The epidemiological model's outputs were integrated into a decision tree structure to calculate health resource consumption and economic outcomes.

Impact:

  • This integrated modeling framework offers a robust method for the economic evaluation of public health interventions.
  • The findings provide insights into the cost-effectiveness of influenza vaccination programs, informing healthcare policy.