Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

Dehingia, Kaushik; Sarmah, Hemanta Kumar; Alharbi, Yamen; Hosseini, K.

doi:10.1186/s13662-021-03621-4

Cited by 17 publications

(5 citation statements)

References 35 publications

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“…Das et al [35] reported that uniform activation of helper T cells may stimulate effector cells and reduce tumor density. In [36][37][38], the authors describe how the tumor-immune interaction is affected by time delay. Rihan et al [39] suggested that time delays and stochastic perturbations greatly disrupt the stability of the tumor-immune system.…”

Section: Introductionmentioning

confidence: 99%

A study on the dynamics of a breast cancer model with discrete-time delay

Das,

Dehingia,

Hinçal

et al. 2024

Phys. Scr.

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This study aims to discuss the impact of discrete-time delay on the anti-tumor immune response against tumor growth, excess levels of estrogen, and the source rate of immune cells in a breast cancer model. The non-negativity and boundedness of the solutions of the model are discussed. The existence of equilibria and their stability are examined. It is found that if the estrogen level is normal and the source rate of immune cells is low, the stability of the model around the co-existing equilibrium switches to instability via a Hopf bifurcation as the time delay increases. To validate the theoretical findings, a few numerical examples have been presented. The main result of this study is that the growth of tumors can be controlled if the immune system quickly generates an anti-tumor immune response. However, if the immune system takes a longer time to generate anti-tumor immune responses, the tumor growth cannot be controlled, and the system becomes unstable, which may result in the further spread of the disease.

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Section: Introductionmentioning

confidence: 99%

A study on the dynamics of a breast cancer model with discrete-time delay

Das,

Dehingia,

Hinçal

et al. 2024

Phys. Scr.

Self Cite

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“…Different approaches can be used in modelling these interacting components. Some models are constructed using deterministic approach [2,9,[30][31][32] while the other based on the stochastic approach [10][11][12]. Irina et.…”

Section: Introductionmentioning

confidence: 99%

The role of noise in the tumour-immune interactions reveals memoryless shifting response

Alharbi

2024

Preprint

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In the present study, the effects of randomness on the model of the immune and cancer cells is discussed. First, we uncover the existence of a bistable response in this interaction where portion of population are cancerous cells. We then discuss how the individual variation within these cells can affect this bistable response. The dominance duration of the tumour and immune cells are highlighted. We calculated the mean of the elimination time of the tumour cells and how can be affected by some key parameters. The analysis reveals that the switching from a stable state to another has a memoryless property.

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“…For example, their growth takes place even in the absence of the signal initiating the growth, continues growing despite the signals stopping their growth. They also attack the surrounding cells of the body among others [7][8][9]. Cancer is regarded as one of the most exhausting illness to treat and hence leads to more deaths than most diseases.…”

Section: Introductionmentioning

confidence: 99%

“…According to [7,20,21] they considered the analysis of a cancer Mathematical model which included the timedelay in the interactivity amidst the Tumor cells and the immune system of the body and their stimulation processes. It analyzed and observed the model dynamics together with changes of crucial restrictions and the effect of time delay on anti -Tumor immune reaction.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for the Effects of Incubation and Chemotherapy on the Dynamics of Tumor Growth

Ogidi,

Wesley,

Daniel

2023

JAMCS

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The application of Mathematical models in simulating processes that are biological in nature has been in effect for a long time. A great number of Mathematical, Computational, Engineering and Physical approaches have been administered to several aspects of development of Tumor, with a view of appreciating how cancer cell population responds to medical intervention. This research therefore considered a Mathematical model for the consequences of incubation and Chemotherapy on Tumor growth dynamics by formulating a deterministic S (susceptible), E (exposed), I (infectious), R (recovered) model using Delay differential equations. The Delay in this case accounted for the duration between the subjection of a cell to cancer virus and the onset of symptomatic disease. Reproduction number (R0) of the model was ascertained using next generation matrix approach. The stability analysis of Cancer Free Equilibrium Point (CFEP) of the model was investigated. MATLAB computer program was used for numerical simulations to validate the analytic results. The investigation and analysis of the consequences of incubation and Chemotherapy on the stability of the equilibrium point was also done. This study of Tumor growth dynamics is significant in that it shall help establish the stage and the extent of cancer spread within the body cells. It shall also help develop a better drug administration procedure as well as providing mechanistic insights. Parameter values used were mostly estimated values. From the numerical analysis, our findings suggest that CFEP is stable when R0 is 0.6667 otherwise unstable.

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Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

Cited by 17 publications

References 35 publications

A study on the dynamics of a breast cancer model with discrete-time delay

A study on the dynamics of a breast cancer model with discrete-time delay

The role of noise in the tumour-immune interactions reveals memoryless shifting response

A Mathematical Model for the Effects of Incubation and Chemotherapy on the Dynamics of Tumor Growth

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