In-host Density-dependent Model of High-risk HPV Virions, Basal Cells, and Lymphocytes T-cells Incorporating Functional Responses

Abstract

Cervical cancer is one of the most common types of cancer and it is caused mostly by high-risk Human Papillomavirus (HPV) and continues to spread at an alarming rate. While HPV impacts have been investigated before, there are currently only a scanty number of mathematical models that account for HPV’s dynamic role in cervical cancer. The objectives were to develop an in-host density-dependent deterministic model for the dynamics implications of basal cells, virions, and lymphocytes incorporating immunity and functional responses. Analyze the model using techniques of epidemiological models such as basic reproduction number and simulate the model using Matlab ODE solver. Six compartments are considered in the model that is; Susceptible cells (S), Infected cells (I), Precancerous cells (P), Cancerous cells (C), Virions (V), and Lymphocytes (L). Next generation matrix (NGM), survival function, and characteristic polynomial method were used to determine the basic reproduction number denoted as 𝑅𝑅0. The findings from this research indicated that the Disease-Free Equilibrium point is locally asymptotically stable whenever 𝑅𝑅0 ∗ < 1 and globally asymptotically stable if 𝑅𝑅0 ∗ ≤ 1 and the Endemic Equilibrium is globally asymptotically stable if 𝑅𝑅0 ∗ > 1. The results obtained show that the progression rate of precancerous cells to cancerous cells (𝜃𝜃) has the most direct impact on the model. The model was able to estimate the longevity of a patient as 10 days when (𝜃𝜃) increases by 8%. The findings of this research will help healthcare providers, public authorities, and non-governmental health groups in creating effective prevention strategies to slow the development of cervical cancer. More research should be done to determine the exact number of cancerous cells that can lead to the death of a cervical cancer patient since this paper estimated a proportion of 75%. Keywords: In-host model, functional responses, stability analysis, simulation and reproduction number.