Waning and boosting: on the dynamics of immune status
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Publication date
2018-05-15
Authors
Diekmann, O.
De Graaf, Wilfred
Kretzschmar, M. E.E.
Teunis, P. F.M.
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Article
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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, Modelling and Simulation, Agricultural and Biological Sciences (miscellaneous), Applied Mathematics
Citation
Diekmann, O, de Graaf, W F, Kretzschmar, M E E & Teunis, P F M 2018, 'Waning and boosting : on the dynamics of immune status', Journal of Mathematical Biology, vol. 77, no. 6-7, pp. 2023-2048. https://doi.org/10.1007/s00285-018-1239-5