Stability analysis of fractional order mathematical model of tumor-immune system interaction

Öztürk, İlhan; Özköse, Fatma

doi:10.1016/j.chaos.2020.109614

Cited by 28 publications

(16 citation statements)

References 36 publications

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“…One of the main reasons for using FODEs is that fractional differential equations have a wider stability region than integer-order equations, that is, fractional-order equations are at least as stable as integer-order equations. Moreover, solutions in fractional-order equations depend on all previous cases [49,59]. It is concluded that Fig.…”

Section: Numerical Simulations and Discussionmentioning

confidence: 75%

“…It implies that the tumor levels may oscillate around an equilibrium point even in absence of any treatment. Such a phenomenon which is known as "Jeff's Phenomenon" has been observed clinically [82] and has arose in many cancer models [58,59]. It is seen that in Fig.…”

Section: Numerical Simulations and Discussionmentioning

confidence: 82%

“…6 and 10 are consistent with real biological phenomena. Figure 6 shows that fractional-order differential equations play the role of time lag or delay term in ordinary differential model and they are naturally related to systems with memory which exists in tumor-immune interactions [59,85]. In Figs.…”

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

“…where t ≥ 0 and r In study [59], the following model was reconstructed by replacing the integer-order derivatives in model (1) with Caputo derivatives:…”

Section: Introductionmentioning

confidence: 99%

“…This consistent can be provided by modifying the parameters involved in the right-hand side of the equations, e.g., raising them to power α. In this context, motivated by [20,59], we have proposed the following the fractional-order system:…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Fractional Modeling of Tumor–Immune System Interaction Related to Lung Cancer with Real Data

et al. 2021

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In this study, we investigate a new fractional-order mathematical model which considers population dynamics among tumor cells-macrophage cells-active macrophage cells, and host cells involving the Caputo fractional derivative. Firstly, the stability of the positive steady state of the model is studied. Subsequently, the conditions for existence and uniqueness of the solutions are examined. Then, the least squares curve fitting method (LSCFM) which is one of the prominent methods for parameter estimation is used to fit the parameters of the model. It is aimed to fit the relevant parameters with the help of the tumor tissue samples which were collected from the patient with non-small cell lung cancer who had chemotherapy-naive hospitalized at Kayseri Erciyes University hospital in Turkey. A total of 12 parameters in the model are estimated using the data of lung tumor cells of this patient for 14 days. Moreover, the numerical simulations are given by considering the different fractional orders and different parameters for the model. So, it is achieved how the change in $$\alpha $$ α affects the dynamic behavior of the system. In the sequel, to point out the advantages of the fractional-order modeling, the memory trace and hereditary traits are taken into consideration. Finally, the interpretations in terms of biological science are provided in conclusion. We believe that this interdisciplinary study will open new doors for other similar studies and will shed light on the studies to be developed on the use of real data in the mathematical modeling of cancer.

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Section: Numerical Simulations and Discussionmentioning

confidence: 75%

Section: Numerical Simulations and Discussionmentioning

confidence: 82%

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

“…where t ≥ 0 and r In study [59], the following model was reconstructed by replacing the integer-order derivatives in model (1) with Caputo derivatives:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Fractional Modeling of Tumor–Immune System Interaction Related to Lung Cancer with Real Data

et al. 2021

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Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

Ahmad,

Abbas,

Inc

et al. 2024

Advanced Biology

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The aim of this study is to analyze and investigate the SARS‐CoV‐2 (SC‐2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC‐2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC‐2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID‐19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC‐2 in the United Kingdom as well as its global effects, also show the actual behavior of SC‐2 which will be helpful to understand the outbreak of SC‐2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies.

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Codimension-one bifurcation analysis and chaos control in a discrete pro- and anti-tumor macrophages model

Niu

Chen

Teng

2023

Int. J. Dynam. Control

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Stability analysis of fractional order mathematical model of tumor-immune system interaction

Cited by 28 publications

References 36 publications

A Fractional Modeling of Tumor–Immune System Interaction Related to Lung Cancer with Real Data

A Fractional Modeling of Tumor–Immune System Interaction Related to Lung Cancer with Real Data

Stability Analysis of SARS‐CoV‐2 with Heart Attack Effected Patients and Bifurcation

Codimension-one bifurcation analysis and chaos control in a discrete pro- and anti-tumor macrophages model

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