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

Infectious Diseases and Their Occurrence01:28

Infectious Diseases and Their Occurrence

Infectious diseases appear in populations through various transmission patterns, influenced by pathogen characteristics, population immunity, environmental conditions, and social behavior. Understanding these patterns is essential for effective public health surveillance and intervention. These categories—sporadic, outbreak, epidemic, pandemic, and endemic—help frame the nature and scope of disease events.Sporadic diseases occur irregularly and infrequently, without a predictable temporal or...
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...
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...
Dose Response Curve: Conventional Versus Nonmonotonic01:21

Dose Response Curve: Conventional Versus Nonmonotonic

The correlation between a drug's dosage and its impact on a biological system is a cornerstone of pharmacology and toxicology. Conventional dose–response curves, which include graded and quantal relationships, are key to this understanding. Graded dose–response curves depict the spectrum of a biological reaction to different doses within an individual, indicating that as the drug dosage increases, so does the intensity of the response. On the other hand, quantal dose–response relationships...
Limits to Natural Selection01:38

Limits to Natural Selection

Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.For one, natural selection can only act upon existing genetic variation. Hypothetically, redtusks may enhance elephant survival by deterring ivory-seeking poachers. However, if there are no gene variants—or alleles—for redtusks, natural selection cannot increase the prevalence of...
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...

You might also read

Related Articles

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

Sort by
Same authorSame journal

Effects of Seasonal Births and Predation on Disease Spread.

Bulletin of mathematical biology·2026
Same author

Beyond distortions: a benchmark for subjective evaluation of image rendering quality.

Scientific reports·2026
Same author

FiloAnalyzer: a deep learning approach for cell filopodia segmentation.

BMC bioinformatics·2026
Same author

Multiscale RGB-Guided Fusion for Hyperspectral Image Super-Resolution.

Journal of imaging·2026
Same author

Common issues and human intervention in object detection from handcrafted features to deep learning: discussion.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025
Same author

Exploring the dynamics of Lotka-Volterra systems: Efficiency, extinction order, and predictive machine learning.

Chaos (Woodbury, N.Y.)·2025

Related Experiment Video

Updated: Jun 14, 2026

In Vitro Assay to Evaluate the Impact of Immunoregulatory Pathways on HIV-specific CD4 T Cell Effector Function
09:26

In Vitro Assay to Evaluate the Impact of Immunoregulatory Pathways on HIV-specific CD4 T Cell Effector Function

Published on: October 15, 2013

Maximal sensitive dependence and the optimal path to epidemic extinction.

Eric Forgoston1, Simone Bianco, Leah B Shaw

  • 1Nonlinear Systems Dynamics Section, Plasma Physics Division, Code 6792, US Naval Research Laboratory, Washington, DC 20375, USA. eric.forgoston.ctr@nrl.navy.mil

Bulletin of Mathematical Biology
|March 31, 2010
PubMed
Summary

Epidemic or species extinction, a rare event, follows an optimal path maximizing extinction probability. This path is linked to finite-time Lyapunov exponents, indicating maximum sensitivity to initial conditions.

More Related Videos

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella
07:11

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Published on: May 13, 2019

Related Experiment Videos

Last Updated: Jun 14, 2026

In Vitro Assay to Evaluate the Impact of Immunoregulatory Pathways on HIV-specific CD4 T Cell Effector Function
09:26

In Vitro Assay to Evaluate the Impact of Immunoregulatory Pathways on HIV-specific CD4 T Cell Effector Function

Published on: October 15, 2013

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella
07:11

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Published on: May 13, 2019

Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Dynamical Systems Theory

Background:

  • Extinction events for epidemics or species are rare occurrences.
  • These events are driven by significant, infrequent stochastic fluctuations.
  • The extinction process, while dynamically unstable, adheres to an optimal trajectory.

Purpose of the Study:

  • To investigate the optimal path of extinction in stochastic epidemic models.
  • To establish a connection between extinction dynamics and finite-time Lyapunov exponents.
  • To demonstrate how a dynamical systems framework naturally leads to the optimal extinction path.

Main Methods:

  • Analysis of stochastic epidemic models within a dynamical systems framework.
  • Utilizing finite-time Lyapunov exponents as a tool to characterize extinction dynamics.
  • Examining the sensitivity of the optimal path to initial conditions.

Main Results:

  • The optimal extinction path is directly related to finite-time Lyapunov exponents.
  • The optimal path exhibits maximum sensitivity to initial conditions.
  • The dynamical systems perspective naturally guides the extinction process toward this optimal path.

Conclusions:

  • Extinction dynamics can be effectively understood and predicted using dynamical systems theory.
  • Finite-time Lyapunov exponents are crucial for identifying and understanding optimal extinction trajectories.
  • This research provides a novel framework for studying extinction events in ecological and epidemiological contexts.