A. S. Novozhilov, F. S. Berezovskaya, E. V. Koonin and G. P. Karev, “Mathematical Modeling of Tumor Therapy with Oncolytic Viruses: Regimes with Complete Tumor Elimination within the Framework of Deterministic Models,” Biology Direct, Vol. 1, No. 1, 2006, p. 6. doi: 10.1186/1745-6150-1-6

has been cited by the following article:

• TITLE: Mathematical Modeling and Analysis of Tumor Therapy with Oncolytic Virus

  AUTHORS: Manju Agarwal, Archana S. Bhadauria

  KEYWORDS: Tumor, Oncolytic Virus, Limit Cycles, Chaotic Behavior, Attractors, Asymptotic Stability

  JOURNAL NAME: Applied Mathematics, Vol.2 No.1, January 30, 2011

  ABSTRACT: In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- tions. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge- Kutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.