title: Angiogenesis model with Erlang distributed delays.
abstract: We consider the model of angiogenesis process proposed by Bodnar and Foryś (2009) with time delays included into the vessels formation and tumour growth processes. Originally, discrete delays were considered, while in the present paper we focus on distributed delays and discuss specific results for the Erlang distributions. Analytical results concerning stability of positive steady states are illustrated by numerical results in which we also compare these results with those for discrete delays.
authors.affiliation: Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. email: emadr@du.edu.eg.
authors.forename: Emad
authors.initials: E
authors.lastname: Attia
authors.forename: Marek
authors.initials: M
authors.lastname: Bodnar
authors.forename: Urszula
authors.initials: U
authors.lastname: Forys
mesh_terms: D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic