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A Computational Study and Stability Analysis of a Mathematical Model for In Vitro Inhibition of Cancer Cell Mutation

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Abstract

Human homeostasis is the body’s ability to physiologically regulate its inner environment to ensure its stability in response to changes in the outside environment. An inability to maintain homeostasis may lead to death or disease, which is caused by a condition known as homeostatic imbalance. Normal cells follow the homeostasis when they proliferate and cancer cells do not. This work deals a model consisting of three reaction–diffusion equations representing in vitro interaction between two drugs. One drug inhibits proliferation of cancerous cells, and the other destroys these cells. The growth of in-vitro cancer cells has been studied using two numerical methods: the Predictor–Corrector and the Operator splitting method. A stability analysis of the model is performed with and without diffusion.

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Acknowledgments

We thank the editor and anonymous reviewers for their constructive comments, which helped us to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Dayton, Dayton, USA

    Muhammad Usman

  2. Department of Mechanical Engineering, University of Dayton, Dayton, USA

    Giacomo Flora

  3. Department of Electrical and Computer Engineering, University of Dayton, Dayton, USA

    Chris Yakopcic

  4. Department of Mathematics and Natural Sciences, Gulf University of Science and Technology, Mishref, Kuwait

    Mudassar Imran

Authors
  1. Muhammad Usman
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  2. Giacomo Flora
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  4. Mudassar Imran
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Correspondence to Muhammad Usman.

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Usman, M., Flora, G., Yakopcic, C. et al. A Computational Study and Stability Analysis of a Mathematical Model for In Vitro Inhibition of Cancer Cell Mutation. Int. J. Appl. Comput. Math 3, 1861–1878 (2017). https://doi.org/10.1007/s40819-016-0201-8

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  • DOI: https://doi.org/10.1007/s40819-016-0201-8

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