Riv. Mat. Univ. Parma, Vol. 12, No. 2, 2021

Hajimohammad Mohammadinejad [a], Saeed Jani [a] and Omid RabieiMotlagh [a]

Mathematical analysis for oncolytic virotherapy
Pages: 221-238
Received: 4 August 2020
Accepted in revised form: 14 June 2021
Mathematics Subject Classification: 37N25, 97M99, 34K20.
Keywords: Hopf bifurcation, Stability, Cancer virotherapy.
Authors address:
[a]:University of Birjand, Birjand, 0098, Iran.

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Abstract: In this paper, we introduce a mathematical model for cancer virotherapy. The model simulates the coeffects of tumor cells and CTLs by considering the time delay of the viral lytic cycle. This delay has been recently seen in some clinical observations when the tumor size changes with a time delay after the virus injection. We investigate the stability of equilibrium points of the model and the corresponding biological interpretation. The model simulates some aspects of the phenomenon which have not been recorded by the former models. For example, a Hopf bifurcation occurs in the delayed model showing an oscillation in the size of the tumor. We indicate natural limitations of the therapy process; for example, the oncolytic virus must be modified such that the time of the delay of the lytic cycle is less than the Hopf bifurcation value.

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