Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control
Joint Authors
Sharma, Swarnali
Samanta, G. P.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-14
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug.
We have considered two immune components—helper (resting) T-cells which stimulate CTLs and convert them into active (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, or ingest the tumor cells.
In our model there are four compartments, namely, tumor cells, active CTL cells, helper T-cells, and chemotherapeutic drug.
We have discussed the behaviour of the solutions of our system.
The dynamical behaviour of our system by analyzing the existence and stability of the system at various equilibrium points is discussed elaborately.
We have set up an optimal control problem relative to the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration.
Here we used a quadratic control to quantify this goal and have considered the administration of chemotherapy drug as control to reduce the spread of the disease.
The important mathematical findings for the dynamical behaviour of the tumor-immune model with control are also numerically verified using MATLAB.
Finally, epidemiological implications of our analytical findings are addressed critically.
American Psychological Association (APA)
Sharma, Swarnali& Samanta, G. P.. 2013. Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control. Journal of Nonlinear Dynamics،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-484768
Modern Language Association (MLA)
Sharma, Swarnali& Samanta, G. P.. Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control. Journal of Nonlinear Dynamics No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-484768
American Medical Association (AMA)
Sharma, Swarnali& Samanta, G. P.. Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control. Journal of Nonlinear Dynamics. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-484768
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484768