Abstract
In this paper we consider a system of delay differential equations as a model for the dynamics of tumor-immune system interaction. We carry out a stability analysis of the proposed model. In particular, we show that the system can have up to two steady states: the tumor free steady state, which always exist, and the tumor persistent steady state, which exists only when the relative rate of increase of the tumor cells exceeds the ratio between the natural proliferation rate and the relative death rate of the effector cells. We also determine an upper bound for the delay, such that stability is preserved. Numerical simulations of the system under different parameter values are performed.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol23iss1pp19-31
- Journal
- Sultan Qaboos University Journal for Science, 23(1), 19
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Hajji, M. A., & Al‐Mdallal, Q. M. (2018). Numerical Simulations of a Delay Model for Immune System-Tumor Interaction. Sultan Qaboos University Journal for Science, 23(1), 19. https://doi.org/10.24200/squjs.vol23iss1pp19-31
MLA 9
Hajji, Mohamed Ali, and Qasem M. Al‐Mdallal. "Numerical Simulations of a Delay Model for Immune System-Tumor Interaction." Sultan Qaboos University Journal for Science, vol. 23, no. 1, 2018, pp. 19. https://doi.org/10.24200/squjs.vol23iss1pp19-31.
Chicago (author–date)
Hajji, Mohamed Ali, and Qasem M. Al‐Mdallal. 2018. "Numerical Simulations of a Delay Model for Immune System-Tumor Interaction." Sultan Qaboos University Journal for Science 23 (1): 19. https://doi.org/10.24200/squjs.vol23iss1pp19-31.
Harvard
Hajji, M. A. and Al‐Mdallal, Q. M. (2018) 'Numerical Simulations of a Delay Model for Immune System-Tumor Interaction', Sultan Qaboos University Journal for Science, 23(1), pp. 19. doi:10.24200/squjs.vol23iss1pp19-31.
Vancouver
Hajji MA, Al‐Mdallal QM. Numerical Simulations of a Delay Model for Immune System-Tumor Interaction. Sultan Qaboos University Journal for Science. 2018;23(1):19. doi:10.24200/squjs.vol23iss1pp19-31
IEEE
M. A. Hajji, and Q. M. Al‐Mdallal, "Numerical Simulations of a Delay Model for Immune System-Tumor Interaction," Sultan Qaboos University Journal for Science, vol. 23, no. 1, pp. 19, 2018, doi: 10.24200/squjs.vol23iss1pp19-31.