Waning and boosting: on the dynamics of immune status

• Type of Material: Article
• Authors: O Diekmann, Utrecht University; WF de Graaf, Utrecht University; MEE Kretzschmar, University Medical Center Utrecht; Peter Teunis, Emory University
• Language: English
• Date: 2018-05-15
• Publisher: Springer (part of Springer Nature): Springer Open Choice Hybrid Journals
• Publication Version: Final Published Version
• Copyright Statement: © The Author(s) 2018
• License: Creative Commons Attribution 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.1007/s00285-018-1239-5
• Title of Journal or Parent Work: Journal of Mathematical Biology
• ISSN: 0303-6812
• Volume: 77
• Issue: 6
• Start Page: 2023
• End Page: 2048
• Keywords: Warning of immunity; Next-generation operator; Renewal equation; Boosting of immunity; Stable distribution
• Research Categories: Health Sciences, Immunology

Abstract

The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller’s fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected. Our main result provides a precise characterization of the stable distribution of immune status.