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S. J. Liao, “Beyond Perturbation: A Review on the Basic Ideas of the Homotopy Analysis Method and Its Applications,” Advanced Mechanics, Vol. 38, No. 1, 2008, pp. 1-34.

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• TITLE: Non-Linear Mathematical Model of the Interaction between Tumor and Oncolytic Viruses

  AUTHORS: Seetharaman Usha, Vairamani Abinaya, Shunmugham Loghambal, Lakshmanan Rajendran

  KEYWORDS: Mathematical Modeling; Non-Linear Differential Equations; Numerical Simulation; Homotopy Analysis Method; Tumor Cells; Oncolytic Viruses

  JOURNAL NAME: Applied Mathematics, Vol.3 No.9, September 27, 2012

  ABSTRACT: A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.