title: The Dynamics of HPV Infection and Cervical Cancer Cells.
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.
authors.affiliation: Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia.|Semarang State University, Semarang, Indonesia.|National Institute for Mathematical and Biological Synthesis (NIMBioS), Knoxville, TN, USA.
authors.forename: Tri Sri Noor
authors.initials: TS
authors.lastname: Asih
authors.affiliation: Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
authors.forename: Suzanne
authors.initials: S
authors.lastname: Lenhart
authors.affiliation: Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Wise
authors.affiliation: Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia.
authors.forename: Lina
authors.initials: L
authors.lastname: Aryati
authors.affiliation: Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia.
authors.forename: F
authors.initials: F
authors.lastname: Adi-Kusumo
authors.affiliation: Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia.
authors.forename: Mardiah S
authors.initials: MS
authors.lastname: Hardianti
authors.affiliation: National Institute for Mathematical and Biological Synthesis (NIMBioS), Knoxville, TN, USA. forde@hws.edu.|Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, NY, USA. forde@hws.edu.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Forde
mesh_terms: D002471:Cell Transformation, Neoplastic / Q000187:drug effects; D002472:Cell Transformation, Viral / Q000187:drug effects; D002584:Cervix Uteri / Q000473:pathology / Q000821:virology; D003198:Computer Simulation; D005260:Female; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D027383:Papillomaviridae / Q000472:pathogenicity*; D030361:Papillomavirus Infections / Q000188:drug therapy / Q000473:pathology / Q000821:virology*; D011230:Precancerous Conditions / Q000188:drug therapy / Q000473:pathology / Q000821:virology; D002583:Uterine Cervical Neoplasms / Q000473:pathology / Q000517:prevention & control / Q000821:virology*
keywords: Cervical cancer; HPV; Mathematical modeling