Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy
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 cance...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/4730715 |
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| author | F. Adi-Kusumo L. Aryati S. Risdayati S. Norhidayah |
| author_facet | F. Adi-Kusumo L. Aryati S. Risdayati S. Norhidayah |
| author_sort | F. Adi-Kusumo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-abe92375aa4c456ebe645a35a9737381 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-abe92375aa4c456ebe645a35a97373812025-02-03T05:44:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/47307154730715Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic EfficacyF. Adi-Kusumo0L. Aryati1S. Risdayati2S. Norhidayah3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaMathematical Education Study Program, FKIP, Universitas Nahdlatul Ulama Kalimantan Selatan, Banjar, IndonesiaMathematical Education Study Program, FKIP, Tridharma University, Balikpapan, IndonesiaWe 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.http://dx.doi.org/10.1155/2020/4730715 |
| spellingShingle | F. Adi-Kusumo L. Aryati S. Risdayati S. Norhidayah Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy International Journal of Mathematics and Mathematical Sciences |
| title | Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy |
| title_full | Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy |
| title_fullStr | Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy |
| title_full_unstemmed | Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy |
| title_short | Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy |
| title_sort | hopf bifurcation on a cancer therapy model by oncolytic virus involving the malignancy effect and therapeutic efficacy |
| url | http://dx.doi.org/10.1155/2020/4730715 |
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