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分数阶隐孢子虫病流行模型的统计估计

A statistical estimation of fractional order cryptosporidiosis epidemic model.

作者信息

Ahmed Nauman, Alhilfi Wissal Audah, AlMansury Hanan A Z, Elwahab Maysaa E A, Tahir Muhammad, Alqasem Ohud A, Iqbal Zafar, Raza Ali, Ceesay Baboucarr, Rafiq Muhammad, Khan Ilyas

机构信息

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1102-2801, Lebanon.

出版信息

Sci Rep. 2025 Apr 23;15(1):14002. doi: 10.1038/s41598-025-92144-z.

DOI:10.1038/s41598-025-92144-z
PMID:40263375
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12015268/
Abstract

In this study, a statistical estimation is done for an epidemic model of cryptosporidiosis by changing it into a fractional order system. The disease-free equilibrium point, and the endemic equilibrium point are the two equilibrium points and Jacobian matrix theory is used to determine stability. The basic reproductive number [Formula: see text] is calculated and examined for its role in disease dynamics and stability analysis. The numerical technique named Grunwald Letnikov non-standard finite difference (GL-NSFD) scheme is designed for solving the fractional epidemic model. To investigate the characteristics and properties of numerical design, a test problem is considered for the simulation. For the underlying system, a non-classical numerical approach is suggested. The state variables cannot be negative because they describe the number of people. The suggested numerical scheme must have the properties of positivity and boundedness. The positivity and boundedness of the fractional order cryptosporidiosis epidemic model are investigated with the help of Laplace and inverse Laplace transformation. Finally, the conclusions of the study are elaborated.

摘要

在本研究中，通过将隐孢子虫病的流行模型转化为分数阶系统，对其进行了统计估计。无病平衡点和地方病平衡点是两个平衡点，利用雅可比矩阵理论确定稳定性。计算了基本再生数[公式：见正文]，并研究了其在疾病动态和稳定性分析中的作用。设计了名为格伦沃尔德-列特尼科夫非标准有限差分（GL-NSFD）格式的数值技术来求解分数阶流行病模型。为了研究数值设计的特性和性质，考虑了一个测试问题进行模拟。对于基础系统，提出了一种非经典数值方法。由于状态变量描述的是人数，所以不能为负。所提出的数值格式必须具有正性和有界性。借助拉普拉斯变换和逆拉普拉斯变换研究了分数阶隐孢子虫病流行模型的正性和有界性。最后，阐述了研究结论。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/77c1cc22273f/41598_2025_92144_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/9a9b6c968ae5/41598_2025_92144_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/008a99584db5/41598_2025_92144_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/0b33b27b33d7/41598_2025_92144_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/b2665a987b05/41598_2025_92144_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/0b0ddc7cf64b/41598_2025_92144_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/5b85661c5883/41598_2025_92144_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/4f0b78297a8f/41598_2025_92144_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/1ca3b424da1b/41598_2025_92144_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/77c1cc22273f/41598_2025_92144_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/9a9b6c968ae5/41598_2025_92144_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/008a99584db5/41598_2025_92144_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/0b33b27b33d7/41598_2025_92144_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/b2665a987b05/41598_2025_92144_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/0b0ddc7cf64b/41598_2025_92144_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/5b85661c5883/41598_2025_92144_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/4f0b78297a8f/41598_2025_92144_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/1ca3b424da1b/41598_2025_92144_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7078/12015268/77c1cc22273f/41598_2025_92144_Fig9_HTML.jpg

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