Related Experiment Video
Updated: Nov 3, 2025
06:56
A Delayed Inoculation Model of Chronic Pseudomonas aeruginosa Wound Infection
Published on: February 20, 2020
8.7K
A Diffusive Sveir Epidemic Model with Time Delay and General Incidence
Jinling Zhou1, Xinsheng Ma1, Yu Yang2
1Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310023 China.
Acta Mathematica Scientia = Shu Xue Wu Li Xue Bao
|June 7, 2021
Summary
A prolonged time delay in a diffusive SVEIR model can eliminate infectiousness. This study establishes threshold dynamics and proves global stability of equilibria using a Nonstandard Finite Difference scheme.
Area of Science:
- Mathematical modeling of infectious diseases
- Epidemiology
- Dynamical systems
Background:
- The spread of infectious diseases is a significant public health concern.
- Mathematical models are crucial for understanding disease dynamics and control.
Purpose of the Study:
- To analyze a delayed diffusive SVEIR (Susceptible-Viral-Infected-Exposed-Recovered) model.
- To investigate the impact of time delays on disease transmission and stability.
Main Methods:
- Establishment of threshold dynamics for the SVEIR model.
- Discretization of the continuous model using a Nonstandard Finite Difference (NSFD) scheme.
- Application of Lyapunov functions to prove global stability of equilibria.
Main Results:
- The threshold dynamics of the delayed diffusive SVEIR model were successfully established.
- Global stability of the model's equilibria was proven using Lyapunov functions.
- Numerical simulations validated the theoretical findings.
Conclusions:
- Time delays in disease models can significantly alter epidemiological outcomes.
- Prolonged time delays were shown to potentially lead to the elimination of infectiousness.
- The NSFD scheme provides a robust method for discretizing and analyzing such models.
Related Concept Videos
01:18Steps in Outbreak Investigation
271
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:
271
01:08Prevalence and Incidence
1.0K
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...
Prevalence indicates the proportion of individuals in a population who have a specific disease or health...
1.0K
01:21Causality in Epidemiology
1.1K
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...
1.1K
02:33Exponential Equations for Modeling Growth
36
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...
36
01:21Diffusion
5.7K
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...
5.7K
01:20Infection
9.5K
When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
9.5K