Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy
Joint Authors
Rachik, Mostafa
El Alami laaroussi, Adil
Hia, Mohamed El
Ghazzali, Rachid
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-09-30
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Despite advanced discoveries in cancerology, conventional treatments by surgery, chemotherapy, or radiotherapy remain ineffective in some situations.
Oncolytic virotherapy, i.e., the involvement of replicative viruses targeting specific tumor cells, opens new perspectives for better management of this disease.
Certain viruses naturally have a preferential tropism for the tumor cells; others are genetically modifiable to present such properties, as the lytic cycle virus, which is a process that represents a vital role in oncolytic virotherapy.
In the present paper, we present a mathematical model for the dynamics of oncolytic virotherapy that incorporates multiple time delays representing the multiple time periods of a lytic cycle.
We compute the basic reproductive ratio R0, and we show that there exist a disease-free equilibrium point (DFE) and an endemic equilibrium point (DEE).
By formulating suitable Lyapunov function, we prove that the disease-free equilibrium (DFE) is globally asymptotically stable if R0<1 and unstable otherwise.
We also demonstrate that under additional conditions, the endemic equilibrium is stable.
Also, a Hopf bifurcation analysis of our dynamic system is used to understand how solutions and their stability change as system parameters change in the case of a positive delay.
To illustrate the effectiveness of our theoretical results, we give numerical simulations for several scenarios.
American Psychological Association (APA)
El Alami laaroussi, Adil& Hia, Mohamed El& Rachik, Mostafa& Ghazzali, Rachid. 2019. Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Computational and Mathematical Methods in Medicine،Vol. 2019, no. 2019, pp.1-12.
https://search.emarefa.net/detail/BIM-1130474
Modern Language Association (MLA)
El Alami laaroussi, Adil…[et al.]. Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Computational and Mathematical Methods in Medicine No. 2019 (2019), pp.1-12.
https://search.emarefa.net/detail/BIM-1130474
American Medical Association (AMA)
El Alami laaroussi, Adil& Hia, Mohamed El& Rachik, Mostafa& Ghazzali, Rachid. Analysis of a Multiple Delays Model for Treatment of Cancer with Oncolytic Virotherapy. Computational and Mathematical Methods in Medicine. 2019. Vol. 2019, no. 2019, pp.1-12.
https://search.emarefa.net/detail/BIM-1130474
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1130474