阿坦加纳-巴莱努分数对登革热动态的最佳控制,使用稳定性分析
Jiraporn Lamwong1, Puntani Pongsumpun2
1Department of Applied Basic Subjects, Thatphanom College, Nakhon Phanom University, Nakhon Phanom, 48000, Thailand.
Computers in biology and medicine
|June 11, 2025
概括
这项研究引入了一种新的分数最佳控制模型,以更好地了解登革热传播动态. 研究结果显示,这种方法可以准确预测疾病的传播,并优化公共卫生控制策略.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 控制理论 控制理论
背景情况:
- 登革热对全球健康构成重大挑战,复杂的传播动态尚未完全被传统模型所捕获.
- 现有的模型往往缺乏结合非局部相互作用,记忆效应和了解疾病传播至关重要的先进控制策略的能力.
- 像泰国这样的地区面临着特殊的挑战,因为复杂的人-蚊子相互作用影响着登革热的传播.
研究的目的:
- 开发和验证一款针对登革热传播动态的创新数学模型.
- 将分数最佳控制问题 (FOCP) 与Atangana-Baleanu分数导数集成,以增强建模能力.
- 准确表示疾病传播,包括记忆效应和非局部相互作用,以改善公共卫生干预措施.
主要方法:
- 人类和蚊子种群的分层建模,将其分为详细的隔间.
- 使用阿坦加纳-巴莱努分数导数 (卡普托感) 应用分数最佳控制问题 (FOCP).
- 在分数顺序微分方程中纳入记忆依赖和非局部相互作用.
主要成果:
- 开发的FOCP模型与登革热,登革热出血热和登革热休克综合征的观察数据密切一致.
- 计算结果在一系列分数顺序 (0.83到1.00) 中一致.
- 敏感性分析确定了关键参数,如咬伤率和初始种群大小,对于有效的疾病控制至关重要.
结论:
- 分数最佳控制问题为模拟复杂的流行病动态,包括登革热提供了强大的框架.
- 该模型为优化公共卫生干预提供了一个强大的工具,旨在降低感染率和相关成本.
- 理论上的全球稳定性分析证实了该模型在预测长期流行病学结果和告知控制策略方面的可靠性.
相关概念视频
01:07Time-Domain Interpretation of PD Control
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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
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01:27Time and frequency -Domain Interpretation of PI Control
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Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
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01:21Linear Approximation in Time Domain
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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01:26Feedback control systems
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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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01:24BIBO stability of continuous and discrete -time systems
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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01:24Frequency-Domain Interpretation of PD Control
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Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
The proportional control gain, combined with the...
The proportional control gain, combined with the...
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