A two-phase within-host model for immune response and its application to serological profiles of pertussis

• Simple phenomenological two-phase within-host model for immune response.
• Estimation of within-host model parameters for pertussis using MCMC methods.
• Threshold antibody level separates clinical from subclinical infections.
• Model predictions correspond with independent observations in literature.

We present a simple phenomenological within-host model describing both the interaction between a pathogen and the immune system and the waning of immunity after clearing of the pathogen. We implement the model into a Bayesian hierarchical framework to estimate its parameters for pertussis using Markov chain Monte Carlo methods. We show that the model captures some essential features of the kinetics of titers of IgG against pertussis toxin. We identify a threshold antibody level that separates a large increase in antibody level upon infection from a small increase and accordingly might be interpreted as a threshold separating clinical from subclinical infections. We contrast predictions of the model with observations reported in the literature and based on independent data and find a remarkable correspondence.