Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Modeling with Differential Equations

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...

Causality in Epidemiology

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...

Population Growth

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.

Exponential Equations for Modeling Growth

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...

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic Models: Compartment Models in Individual and Population Analysis

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 squares (OLS)...

Pharmacodynamic Models: Direct Effect Model and Indirect Response Model

Pharmacodynamic Models: Direct Effect Model and Indirect Response Model

Pharmacodynamic models are essential tools in understanding the relationship between drug concentrations and their effects on biological systems. By characterizing the dynamics of drug action, these models guide dose selection, optimize therapeutic efficacy, and inform the development of new drugs. Two major classes of pharmacodynamic models include direct effect and indirect response models.Direct Effect ModelsDirect effect models describe the immediate relationship between drug concentration...

You might also read

Related Articles

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

Sort by

Same author

Connectivity, conservation and catch: Understanding the effects of dispersal between harvested and protected patches.

Theoretical population biology·2025

Same author

The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models.

Journal of mathematical biology·2023

Same author

Spatial spread of infectious diseases with conditional vector preferences.

Journal of mathematical biology·2023

Same author

Intrinsic nonlinear dynamics drive single-species systems.

Proceedings of the National Academy of Sciences of the United States of America·2022

Same author

Modeling the factors that influence exposure to SARS-CoV-2 on a subway train carriage.

Indoor air·2022

Same author

Towards Building a Sustainable Future: Positioning Ecological Modelling for Impact in Ecosystems Management.

Bulletin of mathematical biology·2021

Search research articles

Related Experiment Video

Updated: May 7, 2026

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

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

Published on: September 2, 2011

Complex dynamics in an eco-epidemiological model.

Andrew M Bate¹, Frank M Hilker

¹Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK, A.M.Bate@bath.ac.uk.

Bulletin of Mathematical Biology

|September 19, 2013

Summary

This summary is machine-generated.

Infectious diseases in predator populations introduce complex ecological dynamics, including bistability and tristability, even when disease spread is limited. These disease-induced shifts can alter ecosystem stability and may lead to irreversible changes.

Related Experiment Videos

Last Updated: May 7, 2026

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

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

Published on: September 2, 2011

Area of Science:

Ecology
Epidemiology
Mathematical Biology

Background:

Infectious diseases can significantly alter ecological system dynamics.
Predator-prey models are crucial for understanding ecosystem stability.

Purpose of the Study:

To investigate the complex dynamics introduced by an SI-type disease in the predator population of a Rosenzweig-MacArthur model.
To explore the impact of disease on ecological stability and regime shifts.

Main Methods:

Numerical solutions of the Rosenzweig-MacArthur model with an SI-type predator disease.
Analysis of bifurcations, periodic solutions, and chaotic dynamics.

Main Results:

Identified saddle-node and subcritical Hopf bifurcations, period-doubling cascades to chaos.
Observed bistability and tristability, including endemic tori, equilibria, and disease-free limit cycles.
Discovered complex dynamics occurring even when the basic reproduction number is less than one.

Conclusions:

Infectious diseases can introduce novel and complex dynamics into predator-prey systems.
Multistability makes the eco-epidemic system highly sensitive to perturbations, potentially causing irreversible regime shifts.
Disease can stabilize or destabilize ecosystems, leading to unexpected outcomes.