Related Experiment Video
Updated: May 5, 2026
20:36
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
8.2K
The effect of time delay in a two-patch model with random dispersal.
1Mathematical Biosciences Institute, The Ohio State University, Ohio, 43210, USA, liao.92@mbi.osu.edu.
Bulletin of Mathematical Biology
|December 4, 2013
Summary
This study analyzes a two-patch model, revealing a critical time delay (τc) that determines population stability. Beyond this threshold, the species
Area of Science:
- Mathematical Biology
- Population Dynamics
- Ecological Modeling
Background:
- Understanding species persistence in fragmented habitats is crucial.
- Time delays in population models can significantly impact stability dynamics.
Purpose of the Study:
- To investigate the effect of time delay on the stability of a single species in a two-patch model.
- To determine the critical time delay threshold for local asymptotic stability.
Main Methods:
- Analysis of a two-patch mathematical model.
- Investigation of local asymptotic stability.
- Determination of critical parameter values for time delay.
Main Results:
- A critical time delay (τc) was identified for a specific range of dispersal rates.
- The unique positive equilibrium is locally asymptotically stable for time delays less than τc.
- The equilibrium becomes unstable for time delays greater than τc.
Conclusions:
- Time delay is a critical factor influencing population stability in spatially structured environments.
- Dispersal rates interact with time delays to shape population dynamics.
- The findings provide insights into the conditions for species persistence in fragmented habitats.
Related Concept Videos
01:14Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model
149
The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A...
149
00:54Distribution and Dispersion
20.9K
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...
20.9K
01:12Two-Compartment Open Model: Extravascular Administration
868
The two-compartment model for extravascular administration represents a drug's absorption and distribution process. It features a central compartment, where the drug is first absorbed, and a peripheral compartment, which illustrates the drug's distribution throughout the body. The rate of change in drug concentration in the central compartment is calculated by three exponents: absorption, distribution, and elimination.
The absorption exponent (ka) indicates the speed at which the drug...
The absorption exponent (ka) indicates the speed at which the drug...
868
01:14Pharmacokinetic–Pharmacodynamic Relationship: Model Components
231
Pharmacokinetic-pharmacodynamic (PK–PD) modeling is essential in drug development and clinical pharmacology. It provides a quantitative framework to predict drug behavior and response over time. This approach integrates pharmacokinetics (PK), which describes the drug's absorption, distribution, metabolism, and excretion, with pharmacodynamics (PD), which characterizes the drug’s biological effects and mechanisms of action.The disposition kinetics of a drug determine its plasma...
231
01:20Compartment Models: Two-Compartment Model
7.1K
The two-compartment model divides the body into central and peripheral compartments to account for varying blood perfusion rates among organs and tissues, affecting drug distribution. The central compartment includes blood and highly perfused tissues with rapid drug distribution, while the peripheral compartment contains tissues with slower drug distribution. After a single IV bolus dose, the drug concentration is high in plasma and low in tissues. The drug distribution between compartments...
7.1K
01:10Interference: Path Lengths
2.5K
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
2.5K