A bi-parametric model for the tumour angiogenesis and anti-angiogenesis therapy

In this work we study a family of phenomenological super-macroscopic models describing the tumour angiogenesis and antiangiogenesis therapy, introduced by Folkman and coworkers [P. Hahnfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumour development under angiogenic signaling: A dynamical theory of tumour growth, treatment response, and postvascular dormancy, Cancer Res. 59 (1999) 4770–4775], and depending on two positive parameters aŒ[0,1] and gŒ[0,5/3]. Here we extend the model by considering not only vessel-disrupting antiangiogenic therapies, but also drugs purely inhibiting the proliferation of endothelial cells, as well as drugs exerting both these actions. By means of cooperativity theory, we show that in order for the family to describe the biological phenomena under study one has to add a further constraint on the two parameters: g≤a. We find conditions for the therapy-induced tumour eradication, and for the local and global stability of the equilibria in the case of lo...