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Dynamical analysis of fractional order model of immunogenic tumors
Arshad, Sadia1,2; Baleanu, Dumitru3,4; Huang, Jianfei5; Tang, Yifa1; Al Qurashi, Maysaa Mohamed6
AbstractIn 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.
KeywordFractional differential equation immune-tumor model stability and bifurcation analysis numerical solutions
Funding Project"Research Center of the Center for Female Scientific and Medical Colleges", Deanship of Scientific Research, King Saud University ; King Saud University
WOS Research AreaThermodynamics ; Engineering
WOS SubjectThermodynamics ; Engineering, Mechanical
WOS IDWOS:000385215200031
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Document Type期刊论文
Corresponding AuthorArshad, Sadia
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.COMSATS Inst Informat Technol, Lahore, Pakistan
3.Cankaya Univ, Fac Arts & Sci, Dept Math, Ankara, Turkey
4.Inst Space Sci, Magurele, Romania
5.Qingdao Univ, Coll Math, Qingdao, Peoples R China
6.King Saud Univ, Dept Math, Riyadh, Saudi Arabia
Recommended Citation
GB/T 7714
Arshad, Sadia,Baleanu, Dumitru,Huang, Jianfei,et al. Dynamical analysis of fractional order model of immunogenic tumors[J]. ADVANCES IN MECHANICAL ENGINEERING,2016,8(7):13.
APA Arshad, Sadia,Baleanu, Dumitru,Huang, Jianfei,Tang, Yifa,&Al Qurashi, Maysaa Mohamed.(2016).Dynamical analysis of fractional order model of immunogenic tumors.ADVANCES IN MECHANICAL ENGINEERING,8(7),13.
MLA Arshad, Sadia,et al."Dynamical analysis of fractional order model of immunogenic tumors".ADVANCES IN MECHANICAL ENGINEERING 8.7(2016):13.
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