Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics

Akimenko, Vitalii V. and Adi-Kusumo, Fajar (2021) Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics. Mathematical Biosciences and Engineering, 18 (5). 6155 – 6177. ISSN 15471063

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Abstract

Stability analysis of an autonomous epidemic model of an age-structured sub-populations of susceptible, infected, precancerous and cancer cells and unstructured sub-population of human papilloma virus (HPV) (SIPCV epidemic model) aims to gain an insight into the features of cervical cancer disease. The model considers the immune functional response of organism to the virus population growing by the HPV-density dependent death rate, while the death rates of infected, precancerous and cancerous cells do not depend on the HPV quantity because the immune system of organism does not respond to its own cells. Interaction between susceptible cells and HPV is described by the Lotka-Voltera incidence rate and leads to the growth of infected cells. Some of infected cells become precancerous cells, and the other apoptosis when viruses leave infected cells and are ready to infect new susceptible cells. Precancerous cells partially become cancer cells with the density-dependent saturated rate. Conditions of existence of the endemic equilibrium of system were obtained. It was proved that this equilibrium is always locally asymptotically stable whenever it exists. We obtained: (i) the conditions of cancer tumor localization (asymptotically stable dynamical regimes), (ii) outbreak of cancer cell population (that may correspond to metastasis), (iii) outbreak of dysplasia (precancerous cells) which induces the outbreak of cancer cells (that may correspond to metastasis). In cases (ii), (iii) the conditions of existence of endemic equilibrium do not hold. All cases are illustrated by numerical experiments. © 2021 the Author(s), licensee AIMS Press.

Item Type: Article
Additional Information: Cited by: 7; All Open Access, Gold Open Access
Uncontrolled Keywords: Alphapapillomavirus; Female; Humans; Incidence; Papillomaviridae; Papillomavirus Infections; Uterine Cervical Neoplasms; Cell culture; Cell death; Cell proliferation; Epidemiology; Pathology; Tumors; Viruses; Age structured model; Asymptotically stable; Cervical cancer cells; Endemic equilibrium; Functional response; Human papilloma virus; Numerical experiments; Stability analysis; Alphapapillomavirus; female; human; incidence; Papillomaviridae; papillomavirus infection; uterine cervix tumor; Diseases
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Mathematics and Natural Sciences > Mathematics Department
Depositing User: Sri JUNANDI
Date Deposited: 02 Sep 2024 03:03
Last Modified: 02 Sep 2024 03:03
URI: https://ir.lib.ugm.ac.id/id/eprint/5919

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