Diffusive pattern formations in three-species nonlinear dynamics of cancer

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.