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

Prevalence and Incidence01:08

Prevalence and Incidence

677
In statistical epidemiology and health sciences, two essential metrics—prevalence and incidence—are fundamental for understanding disease dynamics within a population. These measures enable public health officials, epidemiologists, and researchers to assess the burden of diseases, allocate resources effectively, and design impactful public health policies and interventions.
Prevalence indicates the proportion of individuals in a population who have a specific disease or health...
677
Steps in Outbreak Investigation01:18

Steps in Outbreak Investigation

160
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:
160
Distribution and Dispersion00:54

Distribution and Dispersion

22.1K
To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
22.1K
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

71
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...
71
Poisson Probability Distribution01:09

Poisson Probability Distribution

8.4K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
8.4K
Causality in Epidemiology01:21

Causality in Epidemiology

568
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...
568

You might also read

Related Articles

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

Sort by
Same authorSame journal

A perception-memory PDE framework for seasonal migration dynamics.

Journal of mathematical biology·2026
Same author

Mathematical modelling of methane-induced transitions in aquatic ecosystems.

Journal of mathematical biology·2026
Same author

Derivations of animal movement models with accumulated memory.

Journal of mathematical biology·2026
Same author

Spatiotemporal cholera dynamics with antibiotic resistance and vaccination via demographic-epidemic data in Zimbabwe.

Journal of mathematical biology·2026
Same author

Robust Inverse Reconstruction of Time-Varying Transmission Rates Across Model Structures and Incidence Forms.

Bulletin of mathematical biology·2026
Same author

Starvation-driven diffusion in predator-prey dynamics.

Journal of mathematical biology·2025

Related Experiment Video

Updated: Aug 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

10.7K

Relative prevalence-based dispersal in an epidemic patch model.

Min Lu1, Daozhou Gao2,3, Jicai Huang4

  • 1School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, Hubei, People's Republic of China.

Journal of Mathematical Biology
|March 6, 2023
PubMed
Summary

This study introduces a two-patch SIRS model with nonlinear incidence and prevalence-dependent dispersal rates. It reveals complex disease dynamics, including bistability and oscillations, and shows how dispersal strategies impact disease spread and persistence.

Keywords:
Bogdanov–Takens bifurcationDisease prevalenceHopf bifurcationMixed-mode oscillationsNonconstant dispersalNonlinear incidence rateSIRS patch model

More Related Videos

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

8.8K
Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells
10:21

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

6.2K

Related Experiment Videos

Last Updated: Aug 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

10.7K
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

8.8K
Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells
10:21

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

6.2K

Area of Science:

  • Mathematical epidemiology
  • Dynamical systems theory
  • Population dynamics

Background:

  • Understanding infectious disease dynamics in spatially structured populations is crucial for effective control strategies.
  • Previous models often assume simplified incidence and dispersal rates, limiting their applicability to real-world scenarios.
  • The interplay between local disease transmission and individual movement between patches significantly influences overall disease prevalence.

Purpose of the Study:

  • To develop and analyze a two-patch SIRS epidemiological model incorporating nonlinear incidence and nonconstant, relative-prevalence-dependent dispersal rates.
  • To investigate the complex dynamics, including bifurcations and multiple coexistent states, in both isolated and connected environments.
  • To explore the impact of different dispersal strategies (constant vs. relative prevalence-based) on disease extinction, persistence, and overall prevalence.

Main Methods:

  • Formulation of a two-patch SIRS model with nonlinear incidence and state-dependent dispersal rates.
  • Analysis of local and global dynamics using bifurcation theory (Bogdanov-Takens, Hopf bifurcations) in an isolated environment.
  • Numerical simulations to examine the effects of constant and relative prevalence-based dispersal on disease spread in a connected environment.

Main Results:

  • In isolation, the model exhibits rich dynamics, including cusp and Hopf bifurcations, multiple equilibria, periodic orbits, and bistability.
  • A threshold determines disease extinction versus uniform persistence in a connected environment.
  • Relative prevalence-based dispersal can reduce overall disease prevalence compared to constant dispersal; constant dispersal can increase prevalence.
  • Unidirectional dispersal can lead to complex oscillations or disease extinction in one patch, while relative prevalence-based dispersal can accelerate periodic outbreaks.

Conclusions:

  • The proposed model captures complex epidemiological behaviors arising from nonlinear incidence and adaptive dispersal.
  • Dispersal strategies significantly influence disease dynamics, with relative prevalence-based movement potentially offering a more effective control mechanism.
  • The findings highlight the importance of considering realistic dispersal patterns in epidemiological modeling for predicting and managing disease spread.