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

Abstract

<abstract><p><italic>Human Papillomavirus</italic> (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 $ G_1 $ 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.</p></abstract>

Modeling and Mathematical Analysis of the Dynamics of HPV in Cervical Epithelial Cells: Transient, Acute, Latency, and Chronic Infections

“…A lot of literature has been published [16][17][18][19][20] on the mathematical modeling of viral infections, typically in human immunodeficiency virus, hepatitis B and C, and influenza. Although the literature reports studies on HPV modeling at the cellular level and viral kinetic scenarios [21][22][23][24], they do not show a direct relationship with the types of infection considering the different stratum of the squamous epithelium to show progression or regression of an infection by the HPV. Asih et al [21] proposed a model that considers four compartments: susceptible cells, infected cells, precancerous cells, and cancer cells.…”

“…They analyzed the local stability of the equilibrium points of the model and investigated the parameters that play an important role in the progression toward invasive cancer. Akimenko and Adi-Kusumo [ 22 ], and Sari and Adi-Kusumo [ 23 ] proposed two models of an age-structured subpopulations of susceptible, infected, precancerous, and cancer cells and unstructured subpopulation of HPV that aimed at gaining insight into the disease characteristics of cervical cancer. Verma et al [ 24 ] developed a mathematical model of HIV/HPV coinfection of the oral mucosa.…”

Well-Posedness and a Finite Difference Approximation for a Mathematical Model of HPV-Induced Cervical Cancer

“…Mathematical modeling techniques have been used to investigate the dynamics of cervical cancer, both from epidemiological [3] [4] [5] [6] and cellular [2] [7] [8] [9] [10] viewpoints. Our work here is in the latter context.…”

“…Taking the age of cells into account yields a model of a system of four first-order, nonlinear, partial differential equations and an ordinary differential equation. More recently, Sari et al [9] proposed a modification of the model in [7] that eliminates the ordinary differential equation describing the viral population.…”

“…The mathematical approaches to analyzing those systems have been just as varied. In some cases, such as in [7] [9], stability analysis can be successfully applied to investigate the long-term behavior of solutions. If more knowledge of transient solution behavior or sensitivity analysis is desired, then numerical methods provide a useful tool.…”