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Boosting and waning: on the dynamics of immune status

By Odo Diekmann

Appears in collections : Models in population dynamics and ecology / Modèles en dynamique des populations et écologie, Mathematics of Epidemics, Exposés de recherche

The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by generation expansion (with the generation number corresponding to the number of times an individual became infected). In joint work in progress with Wilfred de Graaf, Peter Teunis and Mirjam Kretzschmar we want to use either the generation expansion or an invariant/stable distribution as the starting point for the efficient computation of coarse statistics.

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Citation data

  • DOI 10.24350/CIRM.V.19044203
  • Cite this video Diekmann Odo (9/6/16). Boosting and waning: on the dynamics of immune status. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19044203
  • URL https://dx.doi.org/10.24350/CIRM.V.19044203


  • [1] de Graaf, W.F., Kretzschmar, M.E.E., Teunis, P.M.F., & Diekmann, O. (2014). A two-phase within host model for immune response and its application to seriological profiles of pertussis. Epidemics, 9, 1-7 - http://dx.doi.org/10.1016/j.epidem.2014.08.002
  • [2] Feller, W. (1971). An introduction to probability theory and its applications. Vol. II. Chapter X, Section 3. New York: John Wiley and Sons - https://www.zbmath.org/?q=an:0219.60003
  • [3] Diekmann, O., Gyllenberg, M., Metz, J.A.J., Nakaoka, S., & de Roos, A.M. (2010). Daphnia revisited : local stability and bifurcation theory for physiologically structured population models explained by way of an example. Journal of Mathematical Biology, 61, 277-318 - http://dx.doi.org/10.1007/s00285-009-0299-y
  • [4] Diekmann, O., Gyllenberg, M., Metz, J.A.J., & Thieme, H.R. (1998). On the formulation and analysis of general deterministic structured population models. I: Linear theory. Journal of Mathematical Biology, 36, 349-388 - http://dx.doi.org/10.1007/s002850050104

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