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All Journal International Journal of Robotics and Control Systems
Shrilekha Elango
Bharathiar University
Control & Systems Engineering Electrical & Electronics Engineering

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Population Dynamics on Fractional Tumor System Using Laplace Transform and Stability Analysis Dhanalakshmi Palanisami; Shrilekha Elango
International Journal of Robotics and Control Systems Vol 3, No 3 (2023)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v3i3.940

Abstract

Modeling is an effective way of using mathematical concepts and tools to represent natural systems and phenomena. Fractional calculus is an essential part of modeling a biological system. Recently, many researchers have been interested in modeling real-time problems mathematically and analyzing them. In this paper, the tumor system under fractional order is considered, and it comprises normal cells, tumor cells and effector-immune cells. By taking chemotherapy drugs into account, the toxicity of the drug and concentration of the drug is also studied in the model. The main objective of this work is to establish the solution for the model using Laplace transform and analyze the stability of the model. Laplace transform, a simple and efficient method, is used in solving the system that proves the existence and uniqueness of the solution. The boundedness of the system is also verified using the Lipschitz condition. Further, the system is solved for numerical values, and the population dynamics of cells are provided for different values of $\alpha$ as a graphical representation. Also, after analyzing the effect of chemotherapy drugs on tumor cells for different $\alpha$'s, which signifies that $\alpha$ = 0.9 provides a sufficient decrease in the dynamics of tumor cells. The main and significant part of this work is presenting that the usage of chemotherapy drugs reduces the number of tumor cells. The importance of the work is that apart from the immune system, chemotherapy drugs play a significant role in destroying tumor cells. The Hyers Ulam stability has a significant application that one need not find the exact solution to when analyzing a Hyers Ulam stable system. Thus, the stability of this tumor model under Caputo fractional order is presented using Hyers-Ulam stability and Hyers-Ulam-Rassias stability.
Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model Dhanalakshmi Palanisami; Shrilekha Elango
International Journal of Robotics and Control Systems Vol 3, No 4 (2023)
Publisher : Association for Scientific Computing Electronics and Engineering (ASCEE)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31763/ijrcs.v3i4.1105

Abstract

This work comprises the spread of Zika virus between humans and mosquitoes as a mathematical simulation under fractional order, which also incorporates the asymptotically infected human population. For determining the solution of the model the fuzzy Laplace transform technique is utilized. By combining fuzzy logic with the Laplace transform, we can analyze systems even when we lack precise information. Further, the sensitivity analysis is performed to validate the model. On top of that the population dynamics of both human and mosquito populations are discussed using numerical data and the graphical result of the model is presented. The main objective of this work is to study the dynamics of the Zika virus and to examine the effect of virus on humans when the transmission occurs between humans and from mosquitoes, under fractional order. The outcome of these comparisons suggests that even by reducing a minute fractional part of transmission through mosquitoes results in a greater reduction of Zika exposed population. The comparisons improve the understanding of fractional level transmission resulting in more effective drug administration to patients. The Hyers-Ulam stability method is a mathematical technique used to study the stability of functional equations. Eventually, Ulam Hyers and Ulam Hyers Rassias stability are employed to assess the stability of the proposed model.
Co-Authors Dhanalakshmi Palanisami