Mathematical Analysis of Virotherapy Treatment for Cancer

Renuka J; Balaganesan P; Vijayakumar PN

Renuka J Assistant Professor, Department of Mathematics, Women’s Christian College, Chennai, Tamil Nadu, India
Balaganesan P Department of Mathematics, AMET Deemed to be University, Chennai, Tamil Nadu, India.
Vijayakumar PN Research Scholar, AMET Deemed to be University, Chennai, Tamil Nadu, India.

Keywords: Non-linear Differential Equations, Cancer Cell Count, Count of Infected Cancer Cells, Count of Dead Cells, Death Rate of Infected Cancer Cells, Homotopy Perturbation Method

Abstract

A virotherapy model for cancer has been identified and analysed in this
article. This mathematical model of cancer virotherapy was developed
by Friedman. It was constructed by means of non-linear differential
equations related to “the count of cancer cells, the count of infected
cancer cells, the count of dead cells, and the count of virus cells that
do not belong to tumour cells”. It also includes parameters for the rate
of viral infection of cancer cells, the proliferation rate of cancer cells,
the removal rate of debris of dead cells, the death rate of infected
cancer cells, and the count of virus particles that are not contained
in cancer cells. The Homotopy Perturbation Method was applied to
solve the non-linear differential equations and was analysed both
qualitatively and numerically. The values of the variation in parameters
were evaluated to investigate the impact of controls on the spread of
cancer cells. Through the numerical and graphical results, the optimal
control, which helps to significantly reduce the impact of cancer cells,
has been discussed. A significant agreement is noted with approximate
analytical results and numerical simulations.

How to cite this article:
Renuka J, Balaganesan P, Vijayakumar PN.
Mathematical Analysis of Virotherapy Treatment
for Cancer. Chettinad Health City Med J.
2023;12(4):81-86.

DOI: https://doi.org/10.24321/2278.2044.202376

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