Growth of nonnecrotic tumors in the presence and absence of inhibitors

H. M. Byrne, M. A. J. Chaplain

    Research output: Contribution to journalArticle

    257 Citations (Scopus)

    Abstract

    In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed range of parameters, which corresponds to a balance between cell proliferation and cell death. Stability analysis, based on a two-timing method, suggests that, where it exists, the nontrivial solution is stable and the trivial solution unstable. Otherwise, the trivial solution is stable. Modification to these characteristic states brought about by the presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the treatment of cancer are also discussed.
    Original languageEnglish
    Pages (from-to)151-181
    Number of pages31
    JournalMathematical Biosciences
    Volume130
    Issue number2
    DOIs
    Publication statusPublished - 1995

    Fingerprint

    Inhibitor
    Tumors
    Tumor
    Trivial
    Nontrivial Solution
    Nutrients
    neoplasms
    Growth
    Neoplasms
    Cell Proliferation
    Stability Analysis
    Timing
    Cancer
    Unstable
    Food
    Cell
    Cell proliferation
    nutrients
    Cell death
    Model

    Keywords

    • Nonnecrotic tumor
    • Inhibitors

    Cite this

    Byrne, H. M. ; Chaplain, M. A. J. / Growth of nonnecrotic tumors in the presence and absence of inhibitors. In: Mathematical Biosciences. 1995 ; Vol. 130, No. 2. pp. 151-181.
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    Growth of nonnecrotic tumors in the presence and absence of inhibitors. / Byrne, H. M.; Chaplain, M. A. J.

    In: Mathematical Biosciences, Vol. 130, No. 2, 1995, p. 151-181.

    Research output: Contribution to journalArticle

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    T1 - Growth of nonnecrotic tumors in the presence and absence of inhibitors

    AU - Byrne, H. M.

    AU - Chaplain, M. A. J.

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    AB - In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed range of parameters, which corresponds to a balance between cell proliferation and cell death. Stability analysis, based on a two-timing method, suggests that, where it exists, the nontrivial solution is stable and the trivial solution unstable. Otherwise, the trivial solution is stable. Modification to these characteristic states brought about by the presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the treatment of cancer are also discussed.

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