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A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages

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Abstract

This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study.

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Authors and Affiliations

  1. Department of Mathematics, Sonari College, Sonari, 785690, Assam, India

    Kaushik Dehingia

  2. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

    Kamyar Hosseini

  3. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey

    Kamyar Hosseini

  4. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Soheil Salahshour

  5. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey

    D. Baleanu

  6. Institute of Space Sciences, Magurele-Bucharest, Romania

    D. Baleanu

  7. Department of Medical Research, China Medical University, Taichung, 40447, Taiwan

    D. Baleanu

Authors
  1. Kaushik Dehingia
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  2. Kamyar Hosseini
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  3. Soheil Salahshour
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  4. D. Baleanu
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Correspondence to Kaushik Dehingia, Kamyar Hosseini or D. Baleanu.

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Dehingia, K., Hosseini, K., Salahshour, S. et al. A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages. Int. J. Appl. Comput. Math 8, 245 (2022). https://doi.org/10.1007/s40819-022-01433-y

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