Related Experiment Video
Updated: Jul 25, 2025
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
8.6K
A Reaction-Diffusion Model with Spatially Inhomogeneous Delays
Yijun Lou1, Feng-Bin Wang2,3,4
1Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong SAR, China.
Journal of Dynamics and Differential Equations
|June 26, 2023
Summary
This study models population growth with uneven maturation times in varied environments. It predicts species extinction if the basic reproduction ratio is below one, and survival otherwise.
Area of Science:
- Mathematical Biology
- Ecology
- Population Dynamics
Background:
- Population growth is influenced by environmental heterogeneity.
- Reaction-diffusion models are crucial for understanding spatial population dynamics.
- Spatially dependent delays present unique challenges in ecological modeling.
Purpose of the Study:
- To develop and analyze a reaction-diffusion model incorporating spatially dependent maturation durations.
- To investigate the impact of spatial heterogeneity and delays on population dynamics.
- To determine conditions for species extinction and persistence.
Main Methods:
- Construction of a reaction-diffusion model with spatially variable parameters and delays.
- Rigorous mathematical analysis including well-posedness and stability.
- Formulation of the basic reproduction ratio (R0).
- Utilizing a novel functional phase space for stability analysis.
Main Results:
- Species extinction is predicted when the basic reproduction ratio (R0) is less than one.
- Uniqueness and global attractivity of a positive equilibrium are established for increasing birth rates when R0 > 1.
- Species permanence is demonstrated for unimodal birth functions when R0 > 1.
Conclusions:
- The model provides insights into population dynamics in heterogeneous environments with spatially varying delays.
- The findings highlight the critical role of the basic reproduction ratio in determining population persistence.
- The developed methodology is applicable to a wider range of ecological models with spatial heterogeneity and time delays.
Related Concept Videos
02:31Multi-Step Reactions
7.4K
Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
7.4K
01:09Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
348
Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...
348
00:57Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models
119
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
119
02:39The Integrated Rate Law: The Dependence of Concentration on Time
35.5K
While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
35.5K
02:20Dynamic Equilibrium
52.0K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
52.0K
01:21Diffusion
4.2K
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...
4.2K