Prevalence Estimation Methods for Time-Dependent Antibody Kinetics of Infected and Vaccinated Individuals: A Markov Chain Approach.

Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalence combine non-trivially to govern antibody levels sampled from a population. Time-dependence and disease prevalence pose considerable modeling challenges that need to be addressed to provide a rigorous mathematical underpinning of the underlying biology. We propose a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for antibody kinetics and demonstrate its use in a setting in which individuals can be infected or vaccinated but not both. We conduct prevalence estimation via transition probability matrices using synthetic data. This approach is ideal to model sequences of infections and vaccinations, or personal trajectories in a population, making it an important first step towards a mathematical characterization of reinfection, vaccination boosting, and cross-events of infection after vaccination or vice versa.