A numerical investigation of nonlinear age-structured tumor with bidirectional proliferative and quiescent phase transitions

The study investigates a nonlinear model that describes the dynamics of populations of tumor cells, with a specific emphasis on the phases of cell proliferation and quiescence. The formulation of the model is determined by the age of the cells and time spend by them in each phase. The nonlinearity arises from the transitions between the proliferative and quiescent phases that are influenced by the age of cells and their total count. We thoroughly investigate the stability characteristic, both local and global, of trivial equilibrium points. To discretize the model, we utilize the discontinuous Galerkin scheme for spatial variables and the explicit Runge–Kutta of order four for time-dependent variables. The effectiveness of the discretized scheme is assessed using the convergence rate outcomes. The validity of our results is confirmed through numerical simulations, which also explore the effects of model paraters.