Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, 11942, Alkharj, Saudi Arabia.
Saveetha School of Engineering, SIMATS, Chennai, India.
Sci Rep. 2024 Jul 15;14(1):16257. doi: 10.1038/s41598-024-66593-x.
In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. The purpose of this work is to investigate the diagnosis and treatment of lung cancer in persons with weakened immune systems by introducing cytokines ( ) and anti-PD-L1 inhibitors. To find the stable position of a recently built system TCD Z, a qualitative and quantitative analysis are taken under sensitive parameters. Reliable bounded findings are ensured by examining the generated system's boundedness, positivity, uniqueness, and local stability analysis, which are the crucial characteristics of epidemic models. The positive solutions with linear growth are shown to be verified by the global derivative, and the rate of impact across every sub-compartment is determined using Lipschitz criteria. Using Lyapunov functions with first derivative, the system's global stability is examined in order to evaluate the combined effects of cytokines and anti-PD-L1 inhibitors on people with weakened immune systems. Reliability is achieved by employing the Mittag-Leffler kernel in conjunction with a fractal-fractional operator because FFO provide continuous monitoring of lung cancer in multidimensional way. The symptomatic and asymptomatic effects of lung cancer sickness are investigated using simulations in order to validate the relationship between anti-PD-L1 inhibitors, cytokines, and the immune system. Also, identify the actual state of lung cancer control with early diagnosis and therapy by introducing cytokines and anti-PD-L1 inhibitors, which aid in the patients' production of anti-cancer cells. Investigating the transmission of illness and creating control methods based on our validated results will both benefit from this kind of research.
为了理解社会中疾病传播的动态，数学公式是必不可少的。本工作旨在通过引入细胞因子（ ）和抗 PD-L1 抑制剂来研究免疫系统较弱的个体的肺癌的诊断和治疗。为了找到最近构建的系统 TCDZ 的稳定位置，在敏感参数下进行了定性和定量分析。通过检查所生成系统的有界性、正定性、唯一性和局部稳定性分析，确保了可靠的有界性结果，这些都是传染病模型的关键特征。通过全局导数验证了具有线性增长的正解的存在性，并使用 Lipschitz 准则确定了每个子区域的影响速度。通过使用具有一阶导数的 Lyapunov 函数，研究了系统的全局稳定性，以评估细胞因子和抗 PD-L1 抑制剂对免疫系统较弱的个体的综合影响。通过使用 Mittag-Leffler 核与分形分数阶算子相结合，实现了可靠性，因为 FFO 以多维方式连续监测肺癌。通过模拟研究了肺癌疾病的症状和无症状影响，以验证抗 PD-L1 抑制剂、细胞因子和免疫系统之间的关系。还通过引入细胞因子和抗 PD-L1 抑制剂来识别肺癌控制的实际状态，以帮助患者产生抗癌细胞。这种研究将有助于研究疾病的传播并基于我们验证的结果制定控制方法。
