Berezansky L, Braverman E, Idels L. Effect of treatment on the global dynamics of delayed pathological angiogenesis models.
J Theor Biol 2014;
363:13-21. [PMID:
25128238 DOI:
10.1016/j.jtbi.2014.08.012]
[Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2014] [Revised: 07/29/2014] [Accepted: 08/05/2014] [Indexed: 11/25/2022]
Abstract
For three different types of angiogenesis models with variable delays, we consider either continuous or impulse therapy that eradicates tumor cells and suppresses angiogenesis. For the cancer-free solution, explicit conditions of global stability for the continuous and impulsive systems are obtained, together with delay-dependent estimates for the rates of decay for the tumor volume and pathological angiogenesis.
Collapse