2013
DOI: 10.1155/2013/608598
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Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control

Abstract: 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.… Show more

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Cited by 32 publications
(37 citation statements)
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“…Mathematical models play an important role in the investigation and the control of the propagation of human infectious diseases, allowing health policy-makers to predict the impact of particular vaccine and treatment programs or to derive more efficient strategies based on different mathematical methods [12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein. Most of mathematical models conventional of the spread of an epidemic have often ignored or underestimated the fact that some infectious diseases can spread easily over large lands.…”
Section: Introductionmentioning
confidence: 99%
“…Mathematical models play an important role in the investigation and the control of the propagation of human infectious diseases, allowing health policy-makers to predict the impact of particular vaccine and treatment programs or to derive more efficient strategies based on different mathematical methods [12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein. Most of mathematical models conventional of the spread of an epidemic have often ignored or underestimated the fact that some infectious diseases can spread easily over large lands.…”
Section: Introductionmentioning
confidence: 99%
“…A simple prey–predator type model for the growth of tumor with discrete time delay in the immune system is considered in Saleem and Agrawal (). A tumor growth model with the effect of tumor–immune interaction and chemotherapeutic drug is also presented and studied in Sharma and Samanta (). In the immune system, both studies assume two immune components helper T cells.…”
Section: Introductionmentioning
confidence: 99%
“…There are some other research works on tumor-immune dynamics [1,3,4,7,12,13,15,31,33,36,38,40]. Also there are some research works on the tumor growth models with optimal control strategies [8,10,11,[16][17][18][19]30,35]. These are very helpful to predict the most effective therapy and strategy to control the spread of diseases minimizing the total drug administered.…”
Section: Introductionmentioning
confidence: 99%