Hopf-bifurcation Analysis of a Delayed Model for the Treatment of Cancer using Virotherapy
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Virotherapy is an effective method for the treatment of cancer. The oncolyticvirus specifically infects the lyse cancer cell without harming normal cells. There is atime delay between the time of interaction of the virus with the tumor cells and the timewhen the tumor cells become infectious and produce new virus particles. Several types ofviruses are used in virotherapy and the delay varies with the type of virus. This delay canplay an important role in the success of virotherapy. Our present study is to explore theimpact of this delay in cancer virotherapy through a mathematical model based on delaydifferential equations. The partial success of virotherapy is guarenteed when one gets astable non-trivial equilibrium with a low level of tumor cells. There exits Hopf-bifurcationby considering the delay as bifurcation parameter. We have estimated the length of delaywhich preserves the stability of the non-trivial equilibrium point. So when the delay isless than a threshold value, we can predict partial success of virotherapy for suitable setsof parameters. Here numerical simulations are also performed to support the analyticalfindings.
Abstract
Virotherapy is an effective method for the treatment of cancer. The oncolyticvirus specifically infects the lyse cancer cell without harming normal cells. There is atime delay between the time of interaction of the virus with the tumor cells and the timewhen the tumor cells become infectious and produce new virus particles. Several types ofviruses are used in virotherapy and the delay varies with the type of virus. This delay canplay an important role in the success of virotherapy. Our present study is to explore theimpact of this delay in cancer virotherapy through a mathematical model based on delaydifferential equations. The partial success of virotherapy is guarenteed when one gets astable non-trivial equilibrium with a low level of tumor cells. There exits Hopf-bifurcationby considering the delay as bifurcation parameter. We have estimated the length of delaywhich preserves the stability of the non-trivial equilibrium point. So when the delay isless than a threshold value, we can predict partial success of virotherapy for suitable setsof parameters. Here numerical simulations are also performed to support the analyticalfindings.
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