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. 2018 Dec;77(6-7):2023-2048.
doi: 10.1007/s00285-018-1239-5. Epub 2018 May 15.

Waning and boosting: on the dynamics of immune status

O Diekmann  1 , W F de Graaf  2 , M E E Kretzschmar  3   4 , P F M Teunis  4   5
Affiliations

Waning and boosting: on the dynamics of immune status

O Diekmann et al. J Math Biol. 2018 Dec.

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.

Keywords: Boosting of immunity; Next-generation operator; Renewal equation; Stable distribution; Waning of immunity.

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