数学建模和最优的控制分析的块性皮肤病在家畜牛
1Department of Mathematics, B. N. MANDAL University (R.J.M. College), Madhepura, Bihar, 852113, India.
Scientific reports
|October 30, 2025
概括
这项研究引入了分数顺序的SIR模型,以了解牛中的块性皮肤病 (LSD). 数学分析和控制策略表明,微积分计算有效地模拟了疾病的传播,缓解努力可以显著减少感染.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 兽医科学是一门兽医科学.
背景情况:
- 状皮肤病 (LSD) 对全球的家畜牛群构成重大威胁.
- 了解LSD的传播动态对于有效的疾病控制至关重要.
- 分数顺序微积分与传统的整数顺序模型相比,提供了一种更细致的方法来建模复杂的生物系统.
研究的目的:
- 开发和分析使用卡普托-法布里齐奥导数的小数级SIR数学模型,用于使用卡普托-法布里齐奥导数在牛中传播LSD.
- 调查分数顺序对疾病动态的影响.
- 推导和评估最佳的控制策略,以减轻LSD的危害.
主要方法:
- 用卡普托-法布里齐奥导数构建一个分数顺序的SIR模型.
- 对模型属性的分析调查,包括正性,边界性和基本复制数.
- 固定点理论的应用,以证明解决方案的存在和独特性.
- 通过Pontryagin的最大原则来推导最佳控制策略.
- 数值模拟用于探索分数顺序动态,并与整数顺序模型进行比较.
主要成果:
- 该模型的基本属性 (积极性,边界性,基本复制数) 通过分析来确定.
- 使用固定点理论证明了解决方案的存在和独特性.
- 数字模拟表明,较低的分数顺序加速疾病传播.
- 最佳的控制策略表明,感染水平大幅降低.
- 对比分析证实了微积分计算在LSD建模中的优越适用性.
结论:
- 分数顺序建模提供了一个更准确的表现,在牛群中块性皮肤疾病的传播动态.
- 建议的最佳控制策略,包括预防和治疗措施,有效地减轻了LSD的传播.
- 这项研究为管理牛群中LSD爆发提供了有价值的见解和实际指导.
更多相关视频
相关概念视频
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
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
282
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
282
01:27Linear Differential Equations
2
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
2
01:29Mathematical Modeling: Problem Solving
249
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
249
01:21Differential Equations: Problem Solving
3
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
3
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
285
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
285