Dynamical behaviour of fractional order tumor-immune model with targeted chemotherapy treatment

Gupta, Praveen Kumar; Dhar, Biplab

doi:10.14419/ijet.v7i2.28.12872

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…These types of models are typically represented by a small set of ordinary differential equations (ODEs). More sophisticated studies, still being general as regards the tumor dynamics, have also included the effect of the host immune system response and/or a treatment, leading to more realistic results, which fit well with experimental data [ 4 , 5 ]. Gupta et al show how certain species of the immune system facilitate tumor destruction, using fractional order derivatives [ 4 ].…”

Section: Introductionmentioning

confidence: 95%

“…More sophisticated studies, still being general as regards the tumor dynamics, have also included the effect of the host immune system response and/or a treatment, leading to more realistic results, which fit well with experimental data [ 4 , 5 ]. Gupta et al show how certain species of the immune system facilitate tumor destruction, using fractional order derivatives [ 4 ]. Elkaranshawy et al includes the immune response and the effect of immunotherapy to make the realistic model [ 5 ].…”

Section: Introductionmentioning

confidence: 95%

“…As can be seen from Table 1 , different models have been developed for the prediction of tumor growth, considering the effects of different factors employing a range of assumptions. For example, many studies consider a single type of generic tumor cells [ 3 , 4 , 5 , 8 , 10 , 11 , 12 , 13 , 14 , 15 ], while others consider separate proliferating, quiescent and necrotic cells within the tumor [ 6 , 7 , 9 , 16 , 17 , 18 ]. The benefit of considering these separate types of cells is a full understanding of intra-tumoral interactions, which prove to be more realistic than a generalized approach.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

2023

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In this study, we propose a set of nonlinear differential equations to model the dynamic growth of avascular stage tumors, considering nutrient supply from underlying tissue, innate immune response, contact inhibition of cell migration, and interactions with a chemotherapeutic agent. The model has been validated against available experimental data from the literature for tumor growth. We assume that the size of the modeled tumor is already detectable, and it represents all clinically observed existent cell populations; initial conditions are selected accordingly. Numerical results indicate that the tumor size and regression significantly depend on the strength of the host immune system. The effect of chemotherapy is investigated, not only within the malignancy, but also in terms of the responding immune cells and healthy tissue in the vicinity of a tumor.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

2023

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A numerical approach of tumor‐immune model with B cells and monoclonal antibody drug by multi‐step differential transformation method

Dhar

Gupta

2020

Math Methods in App Sciences

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Monoclonal antibody (mAb) drugs are used to kill malignant tumors by making them able to see into the immune system. In this article, we developed a mathematical model with the help of tumor‐immune system with antibodies effect and efficacy of mAb drug. We defined the existence of solutions of the model, and by the Lyapunov method, we showed that the solutions are bounded; thereafter, we illustrated the local and global stability phenomenon, which is described by the Lyapunov method and localization of compact invariant sets (LCIS) method for disease‐free equilibrium points including the biological significance. In actual fact, this model suggested some ideas about the malignant tumors reciprocate to mAb drug dosage and its efficacy, eventually to overcome malignancy. It is likely to control the steadiness of the tumor, which is very important for any kind of treatment. The numerical calculations for the proposed model have been carried out by multi‐step differential transformation method (Ms‐DTM). The simulation of the model is depicted through Figures 1–5, which shows the effect of interaction rate of tumor cells and antibodies and dose of the drug for various values of efficacy.

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Numerical Solution of Tumor-Immune Model with Targeted Chemotherapy by Multi Step Differential Transformation Method

Dhar

Gupta

2020

Learning and Analytics in Intelligent Systems

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Dynamical behaviour of fractional order tumor-immune model with targeted chemotherapy treatment

Cited by 8 publications

References 9 publications

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

A numerical approach of tumor‐immune model with B cells and monoclonal antibody drug by multi‐step differential transformation method

Numerical Solution of Tumor-Immune Model with Targeted Chemotherapy by Multi Step Differential Transformation Method

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