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The Dynamics of HPV Infection and Cervical Cancer Cells

Bulletin of Mathematical Biology volume 78, pages 4–20 (2016)Cite this article

Abstract

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.

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Acknowledgments

Thanks to Tim Sparer, Louis J. Gross, Vitaly Ganusov, Jiang Jiang and Kelsey Bratton for useful discussion and assistance.

Author information

Affiliations

  1. Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia

    Tri Sri Noor Asih, Lina Aryati, F. Adi-Kusumo & Mardiah S. Hardianti

  2. Semarang State University, Semarang, Indonesia

    Tri Sri Noor Asih

  3. National Institute for Mathematical and Biological Synthesis (NIMBioS), Knoxville, TN, USA

    Tri Sri Noor Asih & Jonathan Forde

  4. Department of Mathematics, University of Tennessee, Knoxville, TN, USA

    Suzanne Lenhart & Steven Wise

  5. Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, NY, USA

    Jonathan Forde

Authors
  1. Tri Sri Noor Asih
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  2. Suzanne Lenhart
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  3. Steven Wise
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  4. Lina Aryati
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  5. F. Adi-Kusumo
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  6. Mardiah S. Hardianti
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  7. Jonathan Forde
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Corresponding author

Correspondence to Jonathan Forde.

Additional information

Noor Asih’s work was part of her Ph.D. program supported by Ministry of Education and Culture, The Republic of Indonesia. The work of all the authors was partially supported by the National Institute of Mathematical and Biological Synthesis (NIMBioS), an Institute sponsored by National Science Foundation, the US Department of Homeland Security, and the US Department of Agriculture through NSF Awards #EF-0832858 and #DBI-1300426, with additional support from University of Tennessee, Knoxville. Lenhart’s work is also partially supported by the University of Tennessee Center for Business and Economic Research.

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Asih, T.S.N., Lenhart, S., Wise, S. et al. The Dynamics of HPV Infection and Cervical Cancer Cells. Bull Math Biol 78, 4–20 (2016). https://doi.org/10.1007/s11538-015-0124-2

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  • DOI: https://doi.org/10.1007/s11538-015-0124-2

Keywords

  • HPV
  • Cervical cancer
  • Mathematical modeling