Within-host infection dynamics with master equations and the method of moments: A case study of human papillomavirus in the epithelium

TL;DR

This paper develops a stochastic modeling approach using master equations and the method of moments to analyze the infection dynamics of human papillomavirus (HPV) within epithelial tissue, providing insights into disease progression and persistence.

Contribution

It introduces a novel application of master equations and the method of moments to model HPV infection dynamics in epithelial tissue, capturing stochastic effects and informing disease outcomes.

Findings

Model captures infection extinction and persistence.

Provides estimates of viral output over time.

Informs on structural effects on infection dynamics.

Abstract

Master equations provide researchers with the ability to track the distribution over possible states of a system. From these equations, we can summarize the temporal dynamics through a method of moments. These distributions and their moments capture the stochastic nature of a system, which is essential to study infectious diseases. In this paper, we define the states of the system to be the number of infected cells of a given type in the epithelium, the hollow organ tissue in the human body. Epithelium found in the cervix provides a location for viral infections to live and persist, such as human papillomavirus (HPV). HPV is a highly transmissible disease which most commonly affects biological females and has the potential to progress into cervical cancer. By defining a master equation model which tracks the infected cell layer dynamics, information on disease extinction, progression, and viral output can be derived from the method of moments. From this methodology and the outcomes we glean from it, we aim to inform differing states of HPV infected cells, and assess the effects of structural information for each outcome.