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

• Published in: International journal of mathematics and mathematical sciences Vol. 2020; no. 2020; pp. 1 - 8
• Main Authors: Norhidayah, S., Risdayati, S., Aryati, Lina, Adi-Kusumo, F.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 2020; Hindawi; Hindawi Limited; Wiley
• Subjects: Cancer; Cancer therapies; Deactivation; Hopf bifurcation; Immune system; Immunotherapy; Mathematical models; Mutation; Parameters; Predator-prey simulation; Therapy; Viruses
• ISSN: 0161-1712; 1687-0425
• DOI: 10.1155/2020/4730715

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.