title: Effect of treatment on the global dynamics of delayed pathological angiogenesis models.
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.
authors.affiliation: Department of Mathematics, Ben-Gurion University of Negev, Beer-Sheva 84105, Israel.
authors.forename: Leonid
authors.initials: L
authors.lastname: Berezansky
authors.affiliation: Department of Math and Stats, University of Calgary, 2500 University Drive N.W., Calgary, Canada AB T2N 1N4. Electronic address: maelena@math.ucalgary.ca.
authors.forename: Elena
authors.initials: E
authors.lastname: Braverman
authors.affiliation: Department of Math, Vancouver Island University (VIU), 900 Fifth St. Nanaimo, BC, Canada V9S5J5.
authors.forename: Lev
authors.initials: L
authors.lastname: Idels
mesh_terms: D003198:Computer Simulation; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy* / Q000503:physiopathology*; D009389:Neovascularization, Pathologic / Q000188:drug therapy* / Q000503:physiopathology*; D013997:Time Factors
keywords: Angiogenesis; Global stability; Impulsive treatment; Systems of nonlinear nonautonomous delay differential equations