Abstract
A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.
Highlights
The process of tumor growth is one of the most intensively studied processes in recent years
The periodic therapy can be interpreted as a treatment and λ(t) describes the rate of cell apoptosis caused by the periodic therapy
We mainly study how the periodic therapy influences the growth of tumors
Summary
The process of tumor growth is one of the most intensively studied processes in recent years. By the fixed point index theorem, the conditions under which there exist periodic solutions to the model are determined. By the method of steps it is clear that the initial value problem (11), (12) has a unique solution x(t) which exists for all t ≥ 0, because we may rewrite this problem in the following functional form: x (t) = x0 (0) e− ∫0t γ(s)ds
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
