The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises

This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark–Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.

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“…By taking p = x − x * , z = y − x * and h = ĥ + h 1 , from (30) we can obtain the following mapping with an equilibrium point at (0, 0):…”

Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

“…Moreover, they investigated different shell geometries (cylindrical, elliptical, spherical, and hyperbolic) under the biaxial and uniaxial edge density. Duan et al [ 30 ] have discussed a chemotherapy system’s stability analysis in cancer–immune responses. Moreover, their system has more than one fixed point.…”

Section: Introductionmentioning

confidence: 99%

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

Khan

Samreen

Sen

2022

Entropy

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“…As given in detail in Sect. 7, we have numerically integrated the fractional derivatives using the L1 scheme and the solutions of the FODEs for T (t) , A (t) , M (t) , W (t) , have described as the similar way as in (25). Thus, the numerical approximation of the fractional-order derivative of…”

Section: Measurement Of Memory Trace For the Proposed Fractional-order Modelmentioning

confidence: 99%

“…They investigate how the re-oxygenation of hypnotic cells and the radio-sensitivity of radiotherapy influence the effect of tumor radiotherapy. In other study [25], the qualitative analysis of tumor cell-immune cell interaction and chemotherapy with (GWN) Gaussian white noises has been researched. Eftimie and Barelle [26] introduced a model for interactions between lung cancer and macrophages with different phenotypes (M1, M2, M1/M2) with an integer-order differential equation system.…”

Section: Introductionmentioning

confidence: 99%

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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“…MFPT is the mean time for a system to pass from one potential well to another, which has recently garnered a lot of attention from scientific domains [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. It can be used to characterize the transient features of a system, assess the stability of a potential well, and reflect some particular phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Transient properties of grazing ecosystem driven by Lévy noise and Gaussian noise

Mi,

Guo,

Ding

2023

Phys. Scr.

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This paper explores how Lévy noise and Gaussian noise affect the ecological grazing system by using the fourth-order Runge-Kutta method to simulate dynamic system and the Janicki-Weron algorithm to produce Lévy noise. Two deterministic quantities, the mean first passage time (MFPT) and the probability density function (PDF) of the first passage time (FPT), are utilized to explore the transient properties of grazing ecosystem. Our research results show that: (i) The transitions between two alternative stable states can be induced by the Gaussian noise intensity, Lévy noise intensity, Lévy stability index and Lévy skewness parameter. (ii) A higher Lévy noise intensity and a larger Lévy stability index or Lévy skewness parameter make the MFPT from desert state to sustainable vegetated state shorter; a higher Gaussian noise intensity makes it longer, which indicates that increased Lévy noise intensity can mitigate ecosystem degradation; increased Gaussian noise intensity will lead to desertification of vegetation. (iii) For larger Lévy noise intensity, the MFPT from sustainable vegetated state to desert state as a function of Gaussian noise intensity exhibits one maximum value when it transformation from the sustainable vegetated state to the desert state, the noise enhanced stability (NES) phenomena of grazing ecosystems are observed.

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The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises

Cited by 19 publications

References 22 publications

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

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

Transient properties of grazing ecosystem driven by Lévy noise and Gaussian noise

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