Naik Parvaiz Ahmad, Kulachi Muhammad Owais, Ahmad Aqeel, Farman Muhammad, Iqbal Faiza, Taimoor Muhammad, Huang Zhengxin
Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise, China.
Department of Mathematics, Ghazi University D G Khan, Dera Ghazi Khan, Pakistan.
Comput Methods Biomech Biomed Engin. 2024 Sep 20:1-15. doi: 10.1080/10255842.2024.2404540.
The global population has encountered significant challenges throughout history due to infectious diseases. To comprehensively study these dynamics, a novel deterministic mathematical model, TCD Z, is developed for the early detection and treatment of lung cancer. This model incorporates cytokine and anti-PD-L1 inhibitors, enhancing the immune system's anticancer response within five epidemiological compartments. The TCD Z model is analyzed qualitatively and quantitatively, emphasizing local stability given the limited data-a critical component of epidemic modeling. The model is systematically validated by examining essential elements such as equilibrium points, the reproduction number (), stability, and sensitivity analysis. Next-generation techniques based on that track disease transmission rates across the sub-compartments are fed into the system. At the same time, sensitivity analysis helps model how a particular parameter affects the dynamics of the system. The stability on the global level of such therapy agents retrogrades individuals with immunosuppression or treated with and anti-PD-L1 inhibitors admiring the Lyapunov functions' applications. NSFD scheme based on the implicit method is used to find the exact value and is compared with Euler's method and RK4, which guarantees accuracy. Thus, the simulations were conducted in the MATLAB environment. These simulations present the general symptomatic and asymptomatic consequences of lung cancer globally when detected in the middle and early stages, and measures of anticancer cells are implemented including boosting the immune system for low immune individuals. In addition, such a result provides knowledge about real-world control dynamics with and anti-PD-L1 inhibitors. The studies will contribute to the understanding of disease spread patterns and will provide the basis for evidence-based intervention development that will be geared toward actual outcomes.
纵观历史，全球人口因传染病面临了重大挑战。为了全面研究这些动态，开发了一种新型确定性数学模型TCD Z，用于肺癌的早期检测和治疗。该模型纳入了细胞因子和抗PD-L1抑制剂，在五个流行病学隔间内增强免疫系统的抗癌反应。对TCD Z模型进行了定性和定量分析，鉴于数据有限，强调局部稳定性——这是流行病建模的关键组成部分。通过检查平衡点、繁殖数（）、稳定性和敏感性分析等基本要素，系统地验证了该模型。基于追踪子隔间疾病传播率的下一代技术被输入系统。同时，敏感性分析有助于模拟特定参数如何影响系统动态。这种治疗药物在全球层面的稳定性使免疫抑制个体或接受和抗PD-L1抑制剂治疗的个体恢复，这得益于李雅普诺夫函数的应用。基于隐式方法的NSFD方案用于找到精确值，并与欧拉方法和RK4进行比较，以保证准确性。因此，在MATLAB环境中进行了模拟。这些模拟展示了肺癌在全球范围内中早期被检测到时的一般症状性和无症状性后果，以及实施的抗癌细胞措施，包括增强低免疫个体的免疫系统。此外，这样的结果提供了关于和抗PD-L1抑制剂的实际控制动态的知识。这些研究将有助于理解疾病传播模式，并将为基于证据的干预措施开发提供基础，这些措施将针对实际结果。
