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...
Steps in Outbreak Investigation01:18

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:
Causality in Epidemiology01:21

Causality in Epidemiology

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...
Introduction to Epidemiology01:26

Introduction to Epidemiology

Epidemiology, known as the cornerstone of public health, involves studying the distribution and determinants of health-related events in defined populations and applying these insights to control health issues. This is essential for understanding how diseases spread, identifying populations at greater risk, and implementing measures to control or prevent outbreaks. Epidemiology addresses not only infectious diseases but also non-communicable conditions like cancer and cardiovascular disease,...
Population Growth00:57

Population Growth

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.However, realistic environmental conditions limit the number of...
Statistical Methods for Analyzing Epidemiological Data01:25

Statistical Methods for Analyzing Epidemiological Data

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:

You might also read

Related Articles

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

Sort by
Same author

Circular economy: water quality assessment for irrigation purposes in a constructed-wetland scenario.

Scientific reports·2026
Same author

When Few Mosquitoes Are Enough: Dengue outbreaks in non-endemic areas.

One health (Amsterdam, Netherlands)·2026
Same author

Bifurcation analysis of a two-infection transmission model with explicit vector dynamics.

Journal of mathematical biology·2026
Same author

Assessing the spatio-temporal risk of Aedes-borne arboviral diseases in non-endemic regions: The case of Northern Spain.

PLoS neglected tropical diseases·2025
Same author

IoT-Enabled Real-Time Monitoring of Urban Garbage Levels Using Time-of-Flight Sensing Technology.

Sensors (Basel, Switzerland)·2025
Same author

Correction: Forecasting invasive mosquito abundance in the Basque Country, Spain using machine learning techniques.

Parasites & vectors·2025

Related Experiment Video

Updated: Jun 10, 2026

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

Dynamics of epidemiological models.

Alberto Pinto1, Maíra Aguiar, José Martins

  • 1LIAAD-INESC, Porto LA, Portugal. aapinto1@gmail.com

Acta Biotheoretica
|July 28, 2010
PubMed
Summary

This study explores epidemic modeling using stochastic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered-Infected (SIRI) models. Researchers derived dynamic equations and stationary states, approximating quasi-stationary states for SIS models and determining phase transition lines for SIRI models.

More Related Videos

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
12:21

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

Use of the EpiAirway Model for Characterizing Long-term Host-pathogen Interactions
08:12

Use of the EpiAirway Model for Characterizing Long-term Host-pathogen Interactions

Published on: September 2, 2011

Related Experiment Videos

Last Updated: Jun 10, 2026

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

A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
12:21

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

Use of the EpiAirway Model for Characterizing Long-term Host-pathogen Interactions
08:12

Use of the EpiAirway Model for Characterizing Long-term Host-pathogen Interactions

Published on: September 2, 2011

Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Statistical physics

Background:

  • Epidemic models like SIS and SIRI are crucial for understanding disease spread.
  • Stochastic models offer a more realistic approach to disease dynamics.
  • Thresholds determining epidemic appearance require accurate computation.

Purpose of the Study:

  • To derive dynamic equations and stationary states for the stochastic SIS model.
  • To investigate the relationship between the stochastic SIS model and contact processes.
  • To determine phase transition lines for the spatial stochastic SIRI model.

Main Methods:

  • Recursive derivations for moment dynamic equations.
  • Moment closure method to derive stationary states.
  • Mean field and pair approximation for phase transition analysis.
  • Contact process formulation using creation and annihilation operators.
  • Scaling arguments for analytical formula derivation.

Main Results:

  • Steady states of the SIS model approximate quasi-stationary states.
  • Established a connection between the stochastic SIS model and contact processes.
  • Derived analytical formulas for phase transition lines in the SIRI model using pair approximation.

Conclusions:

  • The moment closure method provides accurate approximations for SIS model states.
  • The study offers analytical insights into epidemic thresholds and phase transitions.
  • The findings contribute to a deeper understanding of epidemic dynamics in stochastic environments.