2005/12/09 by Artem S. Novozhilov, Faina Berezovskaya, Novozhilov, Artem S. +5
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Medicine · #Animal Virus Infections Studies #Evolution and Genetic Dynamics #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.q-bio/0512022
openalex publication_date 2005/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of uninfected to infected tumor cells, is proposed to describe the spread of the virus infection in the tumor. One of the main mathematical features of ratio-dependent models is that the origin is a complicated equilibrium point whose characteristics crucially determine the main properties of the model. It is shown that, in a certain area of parameter values, the trajectories of the model form a family of homoclinics to the origin (so-called elliptic sector). Biologically, this means that both infected and uninfected tumor cells can be eliminated with time, and complete recovery is possible as a result of the virus therapy within the framework of deterministic models