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The aim of this article is to help predict the course of lung cancer patients. To make this prediction as close to reality as possible, we used data from lung cancer patients receiving treatment at Erciyes University Hospitals in Kayseri, Turkey. First, we developed a mathematical model considering the cells in the microenvironment of lung cancer tumors with the assistance of Caputo fractional derivatives. Subsequently, we identified the equilibrium points of the proposed mathematical model and examined the coexistence equilibrium point. In addition, we demonstrated the existence and uniqueness of the solutions through the fixed-point theorem. We also investigated the positivity and boundedness of the model's solutions to show whether they are biologically meaningful. Using laboratory experimental results from cancer stem cells isolated from resected tumor tissues of lung cancer patients, we determined the most biologically realistic parameter values through the least squares curve fitting approach. Then, using these parameter values, we performed numerical simulations with the Adams-Bashforth-Moulton predictor-corrector method to validate the theoretical results. We considered different values of fractional derivatives to investigate how the model is affected by fractional derivatives. As a result, we obtained the dynamics and expectations of lung cancer and made predictions specific to individual patients. In our simulations based on the parameter values obtained from actual patient data, it has been observed that after a certain period, both tumor cells and cancer stem cells have been eliminated. Consequently, an increase in normal tissue cells and immune cells has been observed. This implies that the patient in question, and similar behaving patients, will recover and overcome cancer. The findings
from this study provide insights into the dynamics and prognosis of lung
cancer, opening up the possibility for more personalized and effective
approaches to treatment.
The aim of this article is to help predict the course of lung cancer patients. To make this prediction as close to reality as possible, we used data from lung cancer patients receiving treatment at Erciyes University Hospitals in Kayseri, Turkey. First, we developed a mathematical model considering the cells in the microenvironment of lung cancer tumors with the assistance of Caputo fractional derivatives. Subsequently, we identified the equilibrium points of the proposed mathematical model and examined the coexistence equilibrium point. In addition, we demonstrated the existence and uniqueness of the solutions through the fixed-point theorem. We also investigated the positivity and boundedness of the model's solutions to show whether they are biologically meaningful. Using laboratory experimental results from cancer stem cells isolated from resected tumor tissues of lung cancer patients, we determined the most biologically realistic parameter values through the least squares curve fitting approach. Then, using these parameter values, we performed numerical simulations with the Adams-Bashforth-Moulton predictor-corrector method to validate the theoretical results. We considered different values of fractional derivatives to investigate how the model is affected by fractional derivatives. As a result, we obtained the dynamics and expectations of lung cancer and made predictions specific to individual patients. In our simulations based on the parameter values obtained from actual patient data, it has been observed that after a certain period, both tumor cells and cancer stem cells have been eliminated. Consequently, an increase in normal tissue cells and immune cells has been observed. This implies that the patient in question, and similar behaving patients, will recover and overcome cancer. The findings
from this study provide insights into the dynamics and prognosis of lung
cancer, opening up the possibility for more personalized and effective
approaches to treatment.
This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.
An extensive investigation explores the complex terrain of psoriasis, a persistent inflammatory dermatological disorder that impacts between 1% and 3% of the worldwide populace. Acknowledging the intricate interplay between environmental, genetic, and immunological influences on the etiology of psoriasis, the study utilizes sophisticated bibliometric techniques to investigate patterns, gaps in knowledge, and emergent trends within the field. The study utilizes advanced bibliometric techniques to analyze patterns, gaps in knowledge, and emerging trends in the field while acknowledging the intricate interplay between environmental, genetic, and immune-related influences on the etiology of psoriasis. An examination of 18,765 documents from December 2012 to December 2023 was conducted using machine learning techniques and the Scopus database. The explanation for conducting analysis is rooted in its capacity to provide significant perspectives on the dynamic progression of psoriasis research. The study facilitates the identification of significant subject areas, exposes patterns in publication trends, emphasizes influential authors and journals, and outlines the worldwide contributions to the field. The study demonstrates a steady and progressive increase in publications, with significant contributions from the Journal of the American Academy of Dermatology, the British Journal of Dermatology, and the Journal of the European Academy of Dermatology and Venereology. Prominent scholars in research output, such as the United States, China, and Germany, as well as authors including Feldman, Wu, Griffiths, Puig, and Reich K., are identified. Biochemistry, genetics, and molecular biology come to the forefront as esteemed fields that make substantial contributions to the study of psoriasis alongside medicine. This research highlights the interdisciplinary aspects of psoriasis by uncovering knowledge hubs and international collaborations between authors and organizations. The findings highlight the global reach of research on psoriasis and the importance of international cooperation.
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