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Diffusive pattern formations in three-species nonlinear dynamics of cancer

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Abstract

We examine pattern formations of the spatiotemporal dynamics of tumor growth model. The system is modeled by three-species reaction–diffusion equations of healthy cells, cancer cells and acid concentrations. The equilibrium points of the model are determined, the Routh–Hurwitz criteria allowed us to assess the stability of the system by deducing the conditions of existence of Turing models. Numerical results are presented in order to appreciate how biological processes have been affected by the formation of spatiotemporal patterns and highlight the impact of diffusion term on areas of healthy cells, cancer cells and acid concentrations through Turing and non-Turing models. Our results may be used to better describe the relationship between acidity and pattern formation as metastases during tumor growth through different sequence of diffusive cancer dynamics.

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Data Availability Statement

This manuscript has associated data in a data repository [Authors’ comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.]

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Acknowledgements

The authors would like to thank the Editor and to the anonymous Referees for their valuables remarks and suggestions which help us to improve the quality of the present paper.

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Authors and Affiliations

  1. Department of Refining and Petrochemistry, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    S. Issa

  2. Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    B. Tamko. Mbopda & H. P. Ekobena Fouda

  3. Department of Mechanical, Petroleum and Gas Engineering, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    G. Richard Kol

  4. Department of physics and astronomy, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana

    C. Bertrand Tabi

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  1. S. Issa
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Issa, S., Mbopda, B.T., Kol, G.R. et al. Diffusive pattern formations in three-species nonlinear dynamics of cancer. Eur. Phys. J. Plus 138, 496 (2023). https://doi.org/10.1140/epjp/s13360-023-04048-4

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