Waning and boosting: on the dynamics of immune status

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 physiologi...

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Bibliographic Details
Published in:Journal of mathematical biology 2018-12, Vol.77 (6-7), p.2023-2048
Main Authors: Diekmann, O., de Graaf, W. F., Kretzschmar, M. E. E., Teunis, P. F. M.
Format: Article
Language:English
Subjects:
Antibodies - blood
Applications of Mathematics
Communicable Diseases - immunology
Host-Pathogen Interactions - immunology
Humans
Immune status
Immunization, Secondary
Immunologic Memory
Linear Models
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Immunological
Probability
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-018-1239-5