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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 3: 841-860. doi: 10.3934/mbe.2011.8.841
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The replicability of oncolytic virus: Defining conditions in tumor virotherapy

  • 1.
    Mathematics Department, College of William and Mary, Williamsburg, VA 23187
  • Received: 01 June 2010 Accepted: 29 June 2018 Published: 01 June 2011

  • MSC : Primary: 34C23, 34C10; Secondary: 92B99.

  • The replicability of an oncolytic virus is measured by its burst size. The burst size is the number of new viruses coming out from a lysis of an infected tumor cell. Some clinical evidences show that the burst size of an oncolytic virus is a defining parameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolytic virotherapy. The analysis of the model shows that there are two threshold values of the burst size: below the first threshold, the tumor always grows to its maximum (carrying capacity) size; while passing this threshold, there is a locally stable positive equilibrium solution appearing through transcritical bifurcation; while at or above the second threshold, there exits one or three families of periodic solutions arising from Hopf bifurcations. The study suggests that the tumor load can drop to a undetectable level either during the oscillation or when the burst size is large enough.

    Citation: Jianjun Paul Tian. The replicability of oncolytic virus: Defining conditions in tumor virotherapy[J]. Mathematical Biosciences and Engineering, 2011, 8(3): 841-860. doi: 10.3934/mbe.2011.8.841

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  • The replicability of an oncolytic virus is measured by its burst size. The burst size is the number of new viruses coming out from a lysis of an infected tumor cell. Some clinical evidences show that the burst size of an oncolytic virus is a defining parameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolytic virotherapy. The analysis of the model shows that there are two threshold values of the burst size: below the first threshold, the tumor always grows to its maximum (carrying capacity) size; while passing this threshold, there is a locally stable positive equilibrium solution appearing through transcritical bifurcation; while at or above the second threshold, there exits one or three families of periodic solutions arising from Hopf bifurcations. The study suggests that the tumor load can drop to a undetectable level either during the oscillation or when the burst size is large enough.


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