流行病学在离散时间的动态模型,考虑到滞后的过程
1Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kiev, Ukraine.
International journal of dynamics and control
|June 26, 2023
概括
这项研究引入了离散时间流行病模型,为分析真实世界传染病数据提供了比连续微分方程模型更准确的替代方案. 这些差异方程模型简化了计算,并改善了流行病分析.
科学领域:
- 流行病学 流行病学
- 数学建模的数学建模
- 计算动力学是一种计算动力学.
背景情况:
- 连续时间模型如SIR,SEIR和SIRS是流行病学中的标准,但在适应离散统计数据时面临挑战.
- 这些模型使用平均系数,这些系数可能不反映疾病传播动态的每日变化.
- 分散连续模型产生近似值,可能会损害数据拟合和分析的准确性.
研究的目的:
- 提出和验证一种直接在离散时间内使用差异方程制定的通用流行病模型.
- 解决连续模型在准确地表示现实世界的局限性,谨慎地采样流行病数据.
- 为流行病建模提供一个强大的框架,考虑到特定疾病特征和日常变化.
主要方法:
- 基于差异方程系统的通用流行病模型的开发,从一开始就在离散时间内制定.
- 与传统的连续时间微分方程模型 (SIR,SEIR,SIRS) 的比较及其离散近似.
- 分析模型适合适应离散统计数据的分析,考虑到随时间变化的传递系数.
主要成果:
- 与连续模型相比,离散时间差方程模型提供了更准确和更直接的方法来匹配流行病数据.
- 在离散时间的初始表述避免了与离散连续模型相关的计算困难和不准确性.
- 拟议的一般离散时间模型提供了一个灵活的框架,以结合特定的流行病特征和时间变化.
结论:
- 离散时间流行病模型对于分析现实世界,离散地采样传染病数据来说是优越的.
- 在离散时间内直接制定模型可以提高准确性,并简化安装过程.
- 这种方法为了解和预测流行病动态提供了更可靠的基础.
相关概念视频
01:18Steps in Outbreak Investigation
155
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:
155
01:21Causality in Epidemiology
500
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...
500
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
65
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...
65
01:25Statistical Methods for Analyzing Epidemiological Data
426
Epidemiological data primarily involves information on specific populations' occurrence, distribution, and determinants of health and diseases. This data is crucial for understanding disease patterns and impacts, aiding public health decision-making and disease prevention strategies. The analysis of epidemiological data employs various statistical methods to interpret health-related data effectively. Here are some commonly used methods:
426
01:26Introduction to Epidemiology
805
Epidemiology, known as the cornerstone of public health, involves studying the distribution and determinants of health-related events in defined populations and applying these insights to control health issues. This is essential for understanding how diseases spread, identifying populations at greater risk, and implementing measures to control or prevent outbreaks. Epidemiology addresses not only infectious diseases but also non-communicable conditions like cancer and cardiovascular disease,...
805
01:18Models of Health Promotion and Illness Prevention II
1.6K
The person's health status fluctuates continually, varying from being in good health to becoming ill and returning to being healthy. To understand the concept of illness prevention, there are two models. First, the health-illness continuum model is a graphic representation of an individual's wellness. It states that a person is considered healthy in the absence of physical disease and the presence of good emotional health.
The agent-host-environment model states that disease results...
The agent-host-environment model states that disease results...
1.6K