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

Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

140
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...
140
Steps in Outbreak Investigation01:18

Steps in Outbreak Investigation

428
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:
428
Population Growth00:57

Population Growth

27.7K
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.
27.7K
Diffusion01:12

Diffusion

215.3K
Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
215.3K
Diffusion01:21

Diffusion

6.0K
Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
6.0K
Infection01:20

Infection

11.5K
When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
11.5K

You might also read

Related Articles

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

Sort by
Same author

Emergence of spatiotemporal patterns beyond Turing-Hopf bifurcation in semi-arid vegetation systems.

Mathematical biosciences·2026
Same author

A systematic comparison of methodologies for the estimation of the serial interval.

Infectious Disease Modelling·2026
Same author

Hyperedge size-driven multiscale epidemic dynamics on hypergraphs.

Chaos (Woodbury, N.Y.)·2026
Same author

Decoding necrosome assembly: harmonizing signal amplification and attenuation through optimal RIP3 stoichiometry.

Nature communications·2025
Same author

Surveillance of infectious diseases spreading on time-varying multiplex networks.

Infectious Disease Modelling·2025
Same author

Multistability shifts in an aird vegetation system with nonlocal water absorption effect.

Journal of mathematical biology·2025
Same journal

Hysteresis in cavitation emissions during a ramped-then-deramped amplitude sonication: A theoretical and experimental investigation.

Nonlinear dynamics·2026
Same journal

Fluid-structure dynamics of a vibro-impact capsule robot in multiphase intestinal environments.

Nonlinear dynamics·2026
Same journal

Computation of simple invariant solutions in fluid turbulence with the aid of deep learning.

Nonlinear dynamics·2025
Same journal

Swimming dynamics of screw-shaped untethered magnetic robots in confined spaces.

Nonlinear dynamics·2025
Same journal

Bifurcation-based dynamics and internal resonance in micro ring resonators for MEMS applications.

Nonlinear dynamics·2025
Same journal

Optimal control under safety constraints and disturbances: a multi-step, off-policy adaptive dynamic programming approach.

Nonlinear dynamics·2025
See all related articles

Related Experiment Video

Updated: Dec 25, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.3K

Pattern formation of an epidemic model with diffusion.

Gui-Quan Sun1

  • 1Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051 People's Republic of China.

Nonlinear Dynamics
|March 28, 2020
PubMed
Summary
This summary is machine-generated.

This study investigates spatial patterns in epidemic models with nonlinear incidence rates. It reveals how the force of infection influences pattern formation, offering insights into real-world disease spread.

Keywords:
Nonlinear incidence ratesPattern formationSpatial epidemic model

More Related Videos

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

9.1K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.9K

Related Experiment Videos

Last Updated: Dec 25, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.3K
Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

9.1K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.9K

Area of Science:

  • Spatial Epidemiology
  • Mathematical Modeling of Infectious Diseases
  • Pattern Formation in Biological Systems

Background:

  • Spatial variation in disease risk is a key focus of spatial epidemiology.
  • Epidemic spread can create distinct spatial patterns due to factors like localized pathogen dispersal, restricted vectors, or clumped host populations.

Purpose of the Study:

  • To investigate the spatial patterns generated by an epidemic model with nonlinear incidence rates.
  • To determine the conditions for Hopf and Turing bifurcations within the model.
  • To analyze the role of the force of infection (β) in shaping epidemic spatial patterns.

Main Methods:

  • Mathematical analysis to derive conditions for Hopf and Turing bifurcations.
  • Identification of an exact Turing domain in the two-parameter space.
  • Numerical simulations to observe pattern formation as the force of infection (β) varies.

Main Results:

  • Conditions for Hopf and Turing bifurcations were successfully derived.
  • An exact Turing domain was identified within the model's parameter space.
  • The force of infection (β) was shown to be a critical factor, with increasing β leading to diverse spatial patterns.

Conclusions:

  • The study extends understanding of pattern formation in epidemic models.
  • Mathematical analysis and numerical results provide a framework for explaining observed spatial patterns in real-world epidemics.
  • The findings may help explain field observations of disease distribution in specific geographic areas.