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

Area of Science:

• Immunology
• Mathematical Biology
• Epidemiology

Background:

• Immune events like infection and vaccination induce time-dependent antibody responses.
• Population antibody levels result from complex interactions between immune responses and event prevalence.
• Modeling these dynamics presents challenges due to time-dependence and disease prevalence.

Purpose of the Study:

• To develop a rigorous mathematical model for immune event transitions and antibody kinetics.
• To address challenges in modeling time-dependent immune responses and disease prevalence.
• To provide a framework for analyzing sequences of infections and vaccinations.

Main Methods:

• Proposed a time-inhomogeneous Markov chain model for event-to-event transitions.
• Integrated a probabilistic framework for antibody kinetics.
• Utilized synthetic data for prevalence estimation via transition probability matrices.

Main Results:

• Demonstrated a model for individuals experiencing infection or vaccination, but not both.
• Successfully conducted prevalence estimation using the developed transition probability matrices.
• The model effectively captures distinct, time-dependent antibody responses.

Conclusions:

• The proposed Markov chain model offers a robust mathematical underpinning for immune event dynamics.
• This approach is suitable for modeling personal trajectories and sequences of immune events.
• It serves as a foundational step towards characterizing reinfection, vaccine boosting, and cross-events.