Related Experiment Video
Updated: Jan 12, 2026
10:07
Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
Published on: January 31, 2020
6.6K
Rich dynamics in a delayed water borne pathogen model with overexposure
Jinhu Xu1, Yanni Xiao1, Xiaodan Sun1
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, PR China.
Mathematical Biosciences
|October 31, 2025
Summary
This study models delayed waterborne pathogen spread, revealing that overexposure and time delays complicate disease control. Even with a basic reproduction number (R0) below 1, diseases can persist due to backward bifurcation.
Area of Science:
- Mathematical epidemiology
- Infectious disease modeling
- Public health dynamics
Background:
- Waterborne pathogens pose significant public health risks.
- Understanding disease transmission dynamics is crucial for effective control strategies.
- Previous models often simplify complex factors like overexposure and time delays.
Purpose of the Study:
- To formulate and analyze a delayed waterborne pathogen model incorporating overexposure.
- To investigate the threshold dynamics and bifurcation phenomena.
- To assess the impact of overexposure and time delay on disease transmission and stability.
Main Methods:
- Formulation of a delayed differential equation model for waterborne pathogen transmission.
- Analysis of threshold dynamics using the basic reproduction number (R0).
- Theoretical and numerical investigation of backward and Hopf bifurcations.
- Examination of the influence of time delay as a bifurcation parameter.
Main Results:
- The model exhibits backward bifurcation, allowing disease persistence even when R0 < 1.
- Overexposure induces complex dynamics, including stability switches and multiple limit cycles.
- Time delay triggers local and global Hopf bifurcations, leading to stability switches and multiple periodic solutions.
Conclusions:
- Overexposure and time delays significantly complicate waterborne pathogen dynamics.
- These factors contribute to complex behaviors such as endemic persistence and multiple stable states.
- Effective disease control strategies must account for overexposure and time delays to manage complex transmission patterns.
Related Concept Videos
01:25Modeling with Differential Equations
3
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...
3
02:33Exponential Equations for Modeling Growth
198
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...
198
01:18Steps in Outbreak Investigation
481
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:
481
01:21Drug Accumulation During Multiple Dosing: Repetitive IV Injections
244
Calculating drug dosage and accumulation in multiple-dose regimens is crucial for achieving therapeutic efficacy while avoiding toxicity. This involves determining the plasma drug concentrations over time to optimize dosing schedules. The principle of superposition is fundamental in this process, allowing for the prediction of drug concentration in plasma following multiple doses based on single-dose data.The principle of superposition asserts that the plasma concentration-time curves from...
244
02:39The Integrated Rate Law: The Dependence of Concentration on Time
40.8K
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...
40.8K
01:12Two-Compartment Open Model: Extravascular Administration
655
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...
655