Dynamic Analysis of a Mathematical Model of the Anti-Tumor Immune Response

Usman Pagalay, Usman Pagalay and Juhari, Juhari (2024) Dynamic Analysis of a Mathematical Model of the Anti-Tumor Immune Response. ITM Web of Conferences, 58 (01008). pp. 1-13. ISSN 2271-2097

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Abstract

This study discusses the dynamic analysis, the Hopf bifurcation, and numerical simulations. The mathematical model of the anti-tumor immune response consists of three compartments namely Immature T Lymphocytes (L1), Mature T Lymphocytes (L2) and Tumor Cells (T). This research was conducted to represent the behavior between immune cells and tumor cells in the body with five γ conditions. Where γ is the intrinsic growth rate of mature T lymphocytes. This study produces R0 > 1 in conditions 1 to 4 while in condition 5 produces R0 < 1. The disease-free equilibrium point is stable only in condition 5, while the endemic equilibrium point is stable only in conditions 2 and 4. Hopf bifurcation occurs at the endemic equilibrium point. Numerical simulation graph in condition 1 shows that tumor cells will increase uncontrollably. In condition 2 the graph show that the endemic equilibrium point for large tumors is stable. In condition 3 the graph show that there will be a bifurcation from the endemic equilibrium point by the disturbance of the parameter value γ. In condition 4 the graph show the small tumor endemic equilibrium point is stable. Finally, in condition 5, the graph show a stable disease-free equilibrium point.

Item Type:	Journal Article
Keywords:	Dynamic Analysis; Bifurcation; Equilibrium; Numeric Analysis
Subjects:	01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Juhari Juhari
Date Deposited:	19 Feb 2024 14:12

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