Mathematical analysis of a SIPC age-structured model of cervical cancer

Mathematical Biosciences and Engineering

Eminugroho Ratna Sari¹  Lina Aryati²  Fajar Adi-Kusumo² 

[1] 1. Department of Mathematics, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia 2. Department of Mathematics Education, Universitas Negeri Yogyakarta, Yogyakarta 55281, Indonesia;1. Department of Mathematics, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia;

关键词: cervical cancer;    cells dynamics;    age-structured model;    force of infection;    basic reproduction number;    global stability;   

DOI  :  10.3934/mbe.2022281

来源: DOAJ

【 摘 要 】

Human Papillomavirus (HPV), which is the main causal factor of cervical cancer, infects normal cervical cells on the specific cell's age interval, i.e., between the G1 to S phase of cell cycle. Hence, the spread of the viruses in cervical tissue not only depends on the time, but also the cell age. By this fact, we introduce a new model that shows the spread of HPV infections on the cervical tissue by considering the age of cells and the time. The model is a four dimensional system of the first order partial differential equations with time and age independent variables, where the cells population is divided into four sub-populations, i.e., susceptible cells, infected cells by HPV, precancerous cells, and cancer cells. There are two types of the steady state solution of the system, i.e., disease-free and cancerous steady state solutions, where the stability is determined by using Fatou's lemma and solving some integral equations. In this case, we use a non-standard method to calculate the basic reproduction number of the system. Lastly, we use numerical simulations to show the dynamics of the age-structured system.

【 授权许可】

Unknown