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

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....

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Autores principales:	Vitalii V. Akimenko, Fajar Adi-Kusumo
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	sipcv epidemic model age-structured model hpv stability analysis Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/41b78a687c844bbe804018a4b9bac932
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spelling	oai:doaj.org-article:41b78a687c844bbe804018a4b9bac9322021-11-11T01:09:32ZStability analysis of an age-structured model of cervical cancer cells and HPV dynamics10.3934/mbe.20213081551-0018https://doaj.org/article/41b78a687c844bbe804018a4b9bac9322021-07-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021308?viewType=HTMLhttps://doaj.org/toc/1551-0018Stability 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.Vitalii V. AkimenkoFajar Adi-KusumoAIMS Pressarticlesipcv epidemic modelage-structured modelhpvstability analysisBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6155-6177 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	sipcv epidemic model age-structured model hpv stability analysis Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	sipcv epidemic model age-structured model hpv stability analysis Biotechnology TP248.13-248.65 Mathematics QA1-939 Vitalii V. Akimenko Fajar Adi-Kusumo Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
description	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.
format	article
author	Vitalii V. Akimenko Fajar Adi-Kusumo
author_facet	Vitalii V. Akimenko Fajar Adi-Kusumo
author_sort	Vitalii V. Akimenko
title	Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
title_short	Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
title_full	Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
title_fullStr	Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
title_full_unstemmed	Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics
title_sort	stability analysis of an age-structured model of cervical cancer cells and hpv dynamics
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/41b78a687c844bbe804018a4b9bac932
work_keys_str_mv	AT vitaliivakimenko stabilityanalysisofanagestructuredmodelofcervicalcancercellsandhpvdynamics AT fajaradikusumo stabilityanalysisofanagestructuredmodelofcervicalcancercellsandhpvdynamics
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Stability analysis of an age-structured model of cervical cancer cells and HPV dynamics

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