Analysis of a free boundary problem for solid avascular tumor growth with a time delay in regulatory apoptosis

Abstract

In this paper, a mathematical model for solid avascular tumor growth with a time delay in regulatory apoptosis is studied. In the model, two types of cell apoptoses are considered, one is natural apoptosis and the other is regulatory apoptosis. The process of regulatory apoptosis is delayed compared to the processes of proliferation and natural apoptosis. The existence and uniqueness of a solution to the model are proved. The long-time asymptotic behavior of the solutions is studied. The results show that the dynamical behavior of solutions to this mathematical model is similar to that of the corresponding quasi-stationary problem for some special parameter values. Numerical simulations of some special parameter values are also given to verify our results.