Dynamical analysis of fractional order model of immunogenic tumors
Date
2016
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Publisher
Sage Publications Ltd
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Abstract
In this article, we examine the fractional order model of the cytotoxic T lymphocyte response to a growing tumor cell population. We investigate the long-term behavior of tumor growth and explore the conditions of tumor elimination analytically. We establish the conditions for the tumor-free equilibrium and tumor-infection equilibrium to be asymptotically stable and provide the expression of the basic reproduction number. Existence of physical significant tumor-infection equilibrium points is investigated analytically. We show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics and system undergoes saddle-node and transcritical bifurcation based on these parameters. Furthermore, the effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations are presented to illustrate the analytical results.
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Keywords
Fractional Differential Equation, Immune-Tumor Model, Stability And Bifurcation Analysis, Numerical Solutions
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Citation
Arshad, S...et al. (2016). Dynamical analysis of fractional order model of immunogenic tumors. Advance In Mechanical Engineering, 8(7). http://dx.doi.org/10.1177/1687814016656704
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Source
Advance In Mechanical Engineering
Volume
8
Issue
7