Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Authors

  • Aadil Rashid Sheergojri Department of Mathematics and Actuarial Science, B. S.Abdur Rahman Crescent Institute of Science and Technology, Chennai, India. https://orcid.org/0000-0002-7483-8709
  • Pervaiz Iqbal Department of Mathematics and Actuarial Science, B. S.Abdur Rahman Crescent Institute of Science and Technology, Chennai, India. https://orcid.org/0000-0002-3013-7206
  • Praveen Agarwal Department of Mathematics, Anand International College of Engineering, Jaipur, India https://orcid.org/0000-0001-7556-8942
  • Necati Ozdemir Department of Mathematics, Balikesir University, Balikesir, Turkey

DOI:

https://doi.org/10.11121/ijocta.2022.1208

Keywords:

Tumor growth modeling, Fuzzy sets, Gompertz model, Possibility distribution function

Abstract

For treating cancer, tumor growth models have shown to be a valuable resource, whether they are used to develop therapeutic methods paired with process control or to simulate and evaluate treatment processes. In addition, a fuzzy mathematical model is a tool for monitoring the influences of various elements and creating behavioral assessments. It has been designed to decrease the ambiguity of model parameters to obtain a reliable mathematical tumor development model by employing fuzzy logic.The tumor Gompertz equation is shown in an imprecise environment in this study. It considers the whole cancer cell population to be vague at any given time, with the possibility distribution function determined by the initial tumor cell population, tumor net population rate, and carrying capacity of the tumor. Moreover, this work provides information on the expected tumor cell population in the maximum period. This study examines fuzzy tumor growth modeling insights based on fuzziness to reduce tumor uncertainty and achieve a degree of realism. Finally, numerical simulations are utilized to show the significant conclusions of the proposed study.

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Author Biographies

Aadil Rashid Sheergojri, Department of Mathematics and Actuarial Science, B. S.Abdur Rahman Crescent Institute of Science and Technology, Chennai, India.

has received his Bachelor’s degree from the University of Kashmir, Srinagar (J& K), India and Master’s degree from Lovely Professional University Jalandhar Punjab, India. He is presently pursuing Ph.D. in the Department of Mathematics and Actuarial Science from B. S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, India. His research areas include Fuzzy Logic, Fuzzy Mathematics, Mathematical Modelling, Tumor-Dynamics and Numerical Methods.

Pervaiz Iqbal, Department of Mathematics and Actuarial Science, B. S.Abdur Rahman Crescent Institute of Science and Technology, Chennai, India.

is currently working as an Assistant Professor in the Department of Mathematics and Actuarial Science at B.S. Abdur Rahman Crescent Institute of Science \& Technology, Vandalur, Chennai, 600048 since July 2017. Prior to this he was working as a Teaching Assistant in the Department of Mathematics from 2009 to 2010 at Govt. Degree College Women, Kathua, Jammu and Kashmir. He has completed his Doctor's Degree from B.S. Abdur Rahman University, Vandalur, Chennai, in the year 2017. He did his master’s in Applied Mathematics from Baba Ghulam Shah Badshah University, Rajouri, Jammu and Kashmir, in the year 2009. He has published 16 papers in reputed International and National Journals and 2 Book Chapter. And he has presented 23 papers in International Conferences and 15 papers in National Conferences. His broad area of research work is Mathematical Modeling, Optimization Techniques in Operations Research and his interested area is Mathematical Modeling in Biology.

Praveen Agarwal, Department of Mathematics, Anand International College of Engineering, Jaipur, India

was born in Jaipur (India) on August 18, 1979. After completing his schooling, he earned his Master’s degree from Rajasthan University in 2000. In 2006, he earned his Ph. D. (Mathematics) atthe Malviya National Institute of Technology (MNIT) in Jaipur, India, one of the highest ranking universities in India. Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 20 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems. He is an excellent scholar, dedicated teacher, and prolific researcher. He has published 8 research monographs and edited volumes and more than 350 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, UK, Russia, Malaysia and Thailand.In summary of these few inadequate paragraphs, Dr. P. Agarwal is a visionary scientist, educator, and administrator who have contributed to the world through his long service, dedication, and tireless efforts.

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Published

2022-07-14
CITATION
DOI: 10.11121/ijocta.2022.1208
Published: 2022-07-14

How to Cite

Sheergojri, A. R. ., Iqbal, P. ., Agarwal, P., & Ozdemir, N. . (2022). Uncertainty-based Gompertz growth model for tumor population and its numerical analysis. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12(2), 137–150. https://doi.org/10.11121/ijocta.2022.1208

Issue

Vol. 12 No. 2 (2022): IJOCTA

Section

Research Articles

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Copyright (c) 2022 Aadil Rashid Sheergojri, Pervaiz Iqbal, Praveen Agarwal, Necati Ozdemir

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