Probabilistic Modeling of Antibody Kinetics Post Infection and Vaccination: A Markov Chain Approach
About
Understanding the dynamics of antibody levels is crucial for characterizing the time-dependent response to immune events: either infections or vaccinations. The sequence and timing of these events significantly influence antibody level changes. Despite extensive interest in the topic in the recent years and many experimental studies, the effect of immune event sequences on antibody levels is not well understood. Moreover, disease or vaccination prevalence in the population are time-dependent. This, alongside the complexities of personal antibody kinetics, makes it difficult to analyze a sample immune measurement from a population. As a solution, we design a rigorous mathematical characterization in terms of a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for the post-event antibody kinetics of multiple immune events. We demonstrate that this is an ideal model for immune event sequences, referred to as personal trajectories. This novel modeling framework surpasses the susceptible-infected-recovered (SIR) characterizations by rigorously tracking the probability distribution of population antibody response across time. To illustrate our ideas, we apply our mathematical framework to longitudinal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data from individuals with multiple documented infection and vaccination events. Our work is an important step towards a comprehensive understanding of antibody kinetics that could lead to an effective way to analyze the protective power of natural immunity or vaccination, predict missed immune events at an individual level, and inform booster timing recommendations.
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