使用有效的数值方案进行非线性疟疾传播流行病模型的稳定性分析
Jian Jun He1, Abeer Aljohani2, Shahbaz Mustafa3
1School of Humanities and Law, Gannan University of Science and Technology, Ganzhou, 341000, Jiangxi, People's Republic of China.
这项研究使用确定性隔间模型分析了疟疾传播. 非标准的有限差异 (NSFD) 方案在预测疾病传播和稳定性方面被证明是优越的.
科学领域:
- 数学建模的数学建模
- 流行病学 流行病学
- 计算动力学计算动力学
背景情况:
- 疟疾是一个重要的全球健康问题,由由蚊子传播的寄生虫造成的.
- 确定性分隔模型对于理解疾病动态和控制策略至关重要.
研究的目的:
- 分析疟疾传播动态的稳定性,使用确定性隔间模型.
- 为了比较数值方案的有效性,特别是Runge-Kutta顺序4 (RK-4) 和非标准有限差异 (NSFD),用于分析流行病模型.
- 整合时间依赖的控制来减少疟疾的扩散.
主要方法:
- 微分方程的稳定性理论被应用来确定无病和特有平衡.
- 复制数 (R) 是为了评估稳定性条件而计算的.
- 使用RK-4和NSFD方案进行了数值模拟.
- 罗斯-赫尔维茨标准和利亚普诺夫稳定定理用于本地和全球稳定性分析.
主要成果:
- 发现繁殖数 (R) 是一种不对称的稳定条件,适用于无病和特有平衡.
- 与RK-4相比,NSFD方案在所有步骤大小中表现出卓越的准确性和稳定性.
- 在特定条件下 () 证明了无疾病平衡的全球非对称稳定性.
- 在特定条件下,研究了特有平衡的稳定性 ().
结论:
- NSFD方案是分析确定性流行病模型的最合适的数值方法,比RK-4提供更高的性能.
- 该研究提供了理论见解和数值模拟,可以帮助预测和控制疟疾等传染病的传播.
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