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一个非线性数学模型的稳定性分析,用于伤寒热病
Ihsan Ullah Khan1, Shahbaz Mustafa1, Ali Shokri2
1Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, 29050, KPK, Pakistan.
Scientific reports
|September 15, 2023
概括
一个新的非标准有限差异 (NSFD) 方案准确地模拟了伤寒热的动态,超过了Runge-Kutta (RK-4) 方法. 这种NSFD方法保留了可靠的疾病跟踪必不可少的数学特性.
科学领域:
- 数学生物学 数学生物学
- 流行病学 流行病学
- 数字分析 数字分析
背景情况:
- 由于沙门氏菌引起的伤寒热,是通过受污染的食物和水传播的重大公共卫生问题.
- 数学模型对于理解和预测感染性疾病 (如伤寒) 的动态至关重要.
- 精确的数值方法对于模拟这些复杂的疾病模型和确保可靠的预测至关重要.
研究的目的:
- 为了数值地研究一个非线性数学模型对伤寒的动态行为.
- 在模拟模型中,将标准的Runge-Kutta (RK-4) 方案与非标准的有限差异 (NSFD) 方案的有效性进行比较.
- 开发和验证一个动态一致的数值方法,用于伤寒模拟.
主要方法:
- 开发和应用一个条件稳定的Runge-Kutta排序4 (RK-4) 方案.
- 实施一个无条件稳定的非标准有限差异 (NSFD) 方案.
- 两种方案的数值模拟和对比与连续伤寒热病模型.
主要成果:
- RK-4方案仅在较低的步骤大小上表现出动态可靠性,未能保留连续模型的关键特征.
- 该NSFD方案准确地描绘了原始模型,保留了关键的动态特性,如对平衡的趋同和解决方案的积极性.
- 数字模拟证实,离散NSFD方案保留了连续伤寒热病模型的所有动态特征.
结论:
- NSFD方案是模拟伤寒热病动态的强大而有效的数值方法,比RK-4提供更高的准确性和稳定性.
- NSFD方法确保了动态一致性,在所有步骤大小中保持连续模型的基本属性.
- 开发的NSFD计划为跟踪和管理伤寒热病爆发提供了有价值的工具.
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