Panchal Jitendra, Acharya Falguni, Joshi Kanan
Department of Applied Sciences and Humanities, Parul Institute of Engineering and Technology, Parul University, Vadodara, Gujarat India.
Adv Contin Discret Model. 2022;2022(1):27. doi: 10.1186/s13662-022-03700-0. Epub 2022 Mar 26.
This research paper designs the noninteger order SEITR dynamical model in the Caputo sense for tuberculosis. The authors of the article have classified the infection compartment into four different compartments such as newly infected unrecognized individuals, diagnosed patients, highly infected patients, and patients with delays in treatment which provide better detail of the TB infection dynamic. We estimate the model parameters using the least square curve fitting and demonstrate that the proposed model provides a good fit to tuberculosis confirmed cases of India from the year 2000 to 2020. Further, we compute the basic reproduction number as of the model using the next-generation matrix method and the model equilibria. The existence and uniqueness of the approximate solution for the SEITR model is validated using the generalized Adams-Bashforth-Moulton method. The graphical representation of the fractional order model is given to validate the result using the numerical simulation. We conclude that the fractional order model is more realistic than the classical integer order model and provide more detailed information about the real data of the TB disease dynamics.
本研究论文针对结核病设计了Caputo意义下的非整数阶SEITR动力学模型。文章作者将感染隔室分为四个不同的隔室，如新感染未被识别个体、确诊患者、高度感染患者和治疗延迟患者，这能更好地详细描述结核病感染动态。我们使用最小二乘曲线拟合估计模型参数，并证明所提出的模型对印度2000年至2020年的结核病确诊病例拟合良好。此外，我们使用下一代矩阵方法和模型平衡点计算模型的基本再生数为 。使用广义亚当斯 - 巴什福思 - 莫尔顿方法验证了SEITR模型近似解的存在性和唯一性。给出了分数阶模型的图形表示，通过数值模拟验证结果。我们得出结论，分数阶模型比经典整数阶模型更现实，并且能提供有关结核病疾病动态实际数据的更详细信息。
