Time delays in regulatory apoptosis for solid avascular tumour

In the paper, a model of multicellular spheroids dynamics is studied. It can be also interpreted as avascular tumour growth. The model is based on the diffusion of nutrient and mass conservation for two processes cell proliferation and apoptosis. Two types of apoptosis is taken into account-underlying and regulatory apoptosis. It is assumed that the process of regulatory apoptosis is delayed compared to proliferation and underlying apoptosis. ativity of solutions, steady state stability, and existence of periodic solutions are studied in the paper. Computer simulations of solutions are presented. Some conclusions for special values of the model parameters are stated.