Bifurcation Analysis of the Cervical Cancer Cells, Effector Cells, and Il-2 Compounds Interaction Model With Immunotherapy

Adi-Kusumo, Fajar; Winanda, Rara Sandhy

doi:10.17654/ms099060869

Cited by 6 publications

(6 citation statements)

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“…The other interesting problem is studying the immune response of the body for the NPC case. It can be analyzed from the interaction between the tumor cells, the effector cells and the immune cells of the body, see [22] . …”

Section: Discussionmentioning

confidence: 99%

Mathematical modeling of the cells repair regulations in Nasopharyngeal carcinoma

Adi-Kusumo

Wiraya

2016

Mathematical Biosciences

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Section: Discussionmentioning

confidence: 99%

Mathematical modeling of the cells repair regulations in Nasopharyngeal carcinoma

Adi-Kusumo

Wiraya

2016

Mathematical Biosciences

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“…e basic model, the interactions, and the global stability of the equilibria have been introduced in [6,7]. In [8], the authors added the periodic perturbation term in the system that shows the periodic stimulation of the effector cells by the IL-2 compounds and studied the bifurcations of the system due to the variation of the perturbation parameter. e other immunotherapy method for cancer is done by using oncolytic virus; see [9,10].…”

Section: Introductionmentioning

confidence: 99%

Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Suddin

Adi-Kusumo

Aryati

et al. 2021

International Journal of Differential Equations

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Immunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among the cancer cell population, the effector cell population that is a part of the immune system, and cytokines that can be used to stimulate the effector cells called the IL-2 compounds. These interactions depend on both time and spatial position of the cells in the tissue. Mathematically, the spatial movement of the cells is represented by the diffusion terms. We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. In this case, we also consider the steady-state conditions of the system that show the long-time behaviour of these interactions.

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“…Immunotherapy and gene therapy are the cancer treatment methods that provide lower risk of defects for the normal cells. e immunotherapy model for cancer treatment was studied in [4][5][6], where the authors considered the interaction between the cancer cell population, the effector cells, which are a part of the human immune system, and the IL-2 compounds that play a role in stimulating the effector cells. e local analysis of the model was introduced in [5], while the global stability analysis was done in [6].…”

Section: Introductionmentioning

confidence: 99%

“…e local analysis of the model was introduced in [5], while the global stability analysis was done in [6]. Furthermore, the authors in [4] proposed a new model, which was the generalization of the ones in [5,6]. e model in [4] was done by assuming that the interaction between the effector cells and interleukin is no longer a constant, but it can be oscillated with small amplitude; then, they studied the dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the authors in [4] proposed a new model, which was the generalization of the ones in [5,6]. e model in [4] was done by assuming that the interaction between the effector cells and interleukin is no longer a constant, but it can be oscillated with small amplitude; then, they studied the dynamics of the system. Some medical results of the cancer therapy by using oncolytic virus in the medical point of view were reviewed and discussed in [7].…”

Section: Introductionmentioning

confidence: 99%

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Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy

Adi-Kusumo

Aryati

Risdayati

et al. 2020

International Journal of Mathematics and Mathematical Sciences

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We introduce a mathematical model that shows the interaction dynamics between the uninfected and the infected cancer cell populations with oncolytic viruses for the benign and the malignant cancer cases. There are two important parameters in our model that represent the malignancy level of the cancer cells and the efficacy of the therapy. The parameters play an important role to determine the possibility to have successful therapy for cancer. Our model is based on the predator-prey model with logistic growth, functional response, and the saturation effect that show the possibility for the virus to be deactivated and blocked by the human immune system after they reach a certain value. In this paper, we consider the appearance of the Hopf bifurcation on the system to characterize the treatment response based on the malignancy effect of the disease. We employ numerical bifurcation analysis when the value of the malignancy parameter is varied to understand the dynamics of the system.

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Bifurcation Analysis of the Cervical Cancer Cells, Effector Cells, and Il-2 Compounds Interaction Model With Immunotherapy

Cited by 6 publications

References 0 publications

Mathematical modeling of the cells repair regulations in Nasopharyngeal carcinoma

Mathematical modeling of the cells repair regulations in Nasopharyngeal carcinoma

Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions

Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy

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