title: Control exponential growth of tumor cells with slow spread of oncolytic virus.
abstract: Great attention has been paid to cancer therapy by means of oncolytic viruses, but the fast virus-spread, which eliminates all tumor cells, cannot be applied to solid tumors. As slow virus-spread is applied, solid tumors are expected to be controlled but complicated dynamical behaviors appear. In this paper we investigate bifurcations of equilibria in the oncolytic virus dynamics model with exponential growth of tumor cells and slow virus-spread. We find conditions of parameters for saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Those conditions give thresholds for slow virus-spread to control the population of tumor cells within an appropriate range.
authors.affiliation: Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China. Electronic address: siwenmath@163.com.
authors.forename: Wen
authors.initials: W
authors.lastname: Si
authors.affiliation: Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China. Electronic address: matzwn@126.com.
authors.forename: Weinian
authors.initials: W
authors.lastname: Zhang
mesh_terms: D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D050504:Oncolytic Viruses / Q000502:physiology*
keywords: Bifurcation; Cancer growth; Stability