title: A mathematical model verifying potent oncolytic efficacy of M1 virus.
abstract: Motivated by the latest findings in a recent medical experiment [19] which identify a naturally occurring alphavirus (M1) as a novel selective killer targeting zinc-finger antiviral protein (ZAP)-deficient cancer cells, we propose a mathematical model to illustrate the growth of normal cells, tumor cells and the M1 virus with limited nutrient. In order to better understand biological mechanisms, we discuss two cases of the model: without competition and with competition. In the first part, the explicit threshold conditions for the persistence of normal cells (or tumor cells) is obtained accompanying with the biological explanations. The second part indicates that when competing with tumor cells, the normal cells will extinct if M1 virus is ignored; Whereas, when M1 virus is considered, the growth trend of normal cells is similar to the one without competition. And by using uniformly strong repeller theorem, the minimum effective dosage of medication is explicitly found which is not reported in [19]. Furthermore, numerical simulations and corresponding biological interpretations are given to support our results.
authors.affiliation: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou 510006, PR China.
authors.forename: Zizi
authors.initials: Z
authors.lastname: Wang
authors.affiliation: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou 510006, PR China. Electronic address: gzm100@21cn.com.
authors.forename: Zhiming
authors.initials: Z
authors.lastname: Guo
authors.affiliation: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou 510006, PR China.
authors.forename: Huaqin
authors.initials: H
authors.lastname: Peng
mesh_terms: D000524:Alphavirus; D000818:Animals; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms / Q000628:therapy*; D050130:Oncolytic Virotherapy; D050504:Oncolytic Viruses
keywords: M1 virus; Oncolytic virotherapy; Persistence; Stability