The replicability of oncolytic virus: Defining conditions in tumor virotherapy
The replicability of an oncolytic virus is measured byits burst size. The burst size is the number of new viruses comingout from a lysis of an infected tumor cell. Some clinicalevidences show that the burst size of an oncolytic virus is a definingparameter for the success of virotherapy. This articl...
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AIMS Press
2011-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.841 |
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| _version_ | 1832590218454106112 |
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| author | Jianjun Paul Tian |
| author_facet | Jianjun Paul Tian |
| author_sort | Jianjun Paul Tian |
| collection | DOAJ |
| description | The replicability of an oncolytic virus is measured byits burst size. The burst size is the number of new viruses comingout from a lysis of an infected tumor cell. Some clinicalevidences show that the burst size of an oncolytic virus is a definingparameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolyticvirotherapy. 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. |
| format | Article |
| id | doaj-art-d0c23e2f70c148c386dbfc6fe10b515d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d0c23e2f70c148c386dbfc6fe10b515d2025-01-24T02:01:59ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-05-018384186010.3934/mbe.2011.8.841The replicability of oncolytic virus: Defining conditions in tumor virotherapyJianjun Paul Tian0Mathematics Department, College of William and Mary, Williamsburg, VA 23187The replicability of an oncolytic virus is measured byits burst size. The burst size is the number of new viruses comingout from a lysis of an infected tumor cell. Some clinicalevidences show that the burst size of an oncolytic virus is a definingparameter for the success of virotherapy. This article analyzes a basic mathematical model that includes burst size for oncolyticvirotherapy. 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.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.841hopf bifurcation.virotherapyburst size |
| spellingShingle | Jianjun Paul Tian The replicability of oncolytic virus: Defining conditions in tumor virotherapy Mathematical Biosciences and Engineering hopf bifurcation. virotherapy burst size |
| title | The replicability of oncolytic virus: Defining conditions in tumor virotherapy |
| title_full | The replicability of oncolytic virus: Defining conditions in tumor virotherapy |
| title_fullStr | The replicability of oncolytic virus: Defining conditions in tumor virotherapy |
| title_full_unstemmed | The replicability of oncolytic virus: Defining conditions in tumor virotherapy |
| title_short | The replicability of oncolytic virus: Defining conditions in tumor virotherapy |
| title_sort | replicability of oncolytic virus defining conditions in tumor virotherapy |
| topic | hopf bifurcation. virotherapy burst size |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.841 |
| work_keys_str_mv | AT jianjunpaultian thereplicabilityofoncolyticvirusdefiningconditionsintumorvirotherapy AT jianjunpaultian replicabilityofoncolyticvirusdefiningconditionsintumorvirotherapy |