Mathematical Biosciences and Engineering, 2011, 8(3): 841-860. doi: 10.3934/mbe.2011.8.841.

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

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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

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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Keywords Hopf bifurcation.; Virotherapy; burst size

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


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