Oncolytic virotherapy is emerging as a promising new method for cancer treatment. In the present study, we propose and analyze a mathematical model for treatment of cancer by using oncolytic virotherapy. Here, it is assumed that the growth of tumor cells follows logistic growth and the interaction between tumor cells and viruses is of saturation type. Additionally, the removal rates of uninfected and virus-infected tumor cells due to CTL’s are also of saturation type. The basic reproduction numbers and different equilibria of the model are computed. The local stability of the equilibria is also discussed. Numerical simulation is also performed and it is found that for some set of parameters model system exhibits periodic oscillations. In this case it is not easy to predict the success of virotherapy. Finally, the model is extended to stochastic model and numerical simulation is performed to compare the results of deterministic and stochastic model. © 2019, © 2019 Taylor &amp; Francis Group, LLC.

Mini Ghosh

Mathematics

School of Advanced Sciences

Chennai Campus

Rajalakshmi M

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Modeling treatment of cancer using oncolytic virotherapy with saturated incidence

Stochastic Analysis and Applications

Virotherapy is an effective strategy in cancer treatment. It eliminates tumor cells without harming the healthy cells. In this article, a deterministic mathematical model to understand the dynamics of tumor cells in response to virotherapy is formulated and analyzed by incorporating cytotoxic T lymphocytes (CTLs). The basic reproduction number and the immune response reproduction number are computed and different equilibria of the proposed model are found. The local stability of different equilibria is discussed in detail. Further, the proposed model is extended to stochastic model. Numerical simulation is performed for both deterministic and stochastic models. It is observed that when both the reproduction numbers are greater than one, which corresponds to existence of unique nontrivial equilibrium point, dynamics of deterministic and stochastic models are almost same. The deterministic model shows a very complex dynamics when one or both the reproduction numbers are below one. The system exhibits both backward bifurcation and Hopf-bifurcation for suitable sets of parameters and in this situation it is not easy to predict the dynamics of cancer cells and virus particles. The existence of backward bifurcation demonstrates the fact that partial success of virotherapy can be achieved even if the immune response reproduction number is less than one. © 2018, © 2018 Taylor &amp; Francis Group, LLC.

Modeling treatment of cancer using virotherapy with generalized logistic growth of tumor cells

Japanese Journal of Clinical Oncology

Oncolytic virus therapy in Japan: progress in clinical trials and future perspectives

Journal of Theoretical Biology

An Îto stochastic differential equations model for the dynamics of the MCF-7 breast cancer cell line treated by radiotherapy

Dynamics of tumor virotherapy: A deterministic and stochastic model approach

Journal of Controlled Release

Polymeric oncolytic adenovirus for cancer gene therapy

Journal	Stochastic Analysis and Applications
Publisher	Informa UK Limited
ISSN	0736-2994
Open Access	0