H 2 Boosting and waning: on the dynamics of immune status

Auteurs : Diekmann, Odo (Auteur de la Conférence)
CIRM (Editeur )

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model ingredients random variable and kernel renewal equation dynamical system perspective stable distribution travel time Questions of the audience

Résumé : 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.

Codes MSC :
45D05 - Volterra integral equations
60J75 - Jump processes
92D30 - Epidemiology

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 13/09/2016
    Date de captation : 06/09/2016
    Sous collection : Research talks
    arXiv category : Quantitative Biology ; Dynamical Systems
    Domaine : Dynamical Systems & ODE ; Mathematics in Science & Technology
    Format : MP4 (.mp4) - HD
    Durée : 00:58:03
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-09-06_Diekmann.mp4

Informations sur la rencontre

Nom de la rencontre : Models in population dynamics and ecology / Modèles en dynamique des populations et écologie
Organisateurs de la rencontre : Langlais, Michel ; Malchow, Horst ; Petrovskii, Sergei ; Poggiale, Jean-Christophe
Dates : 05/09/2016 - 09/09/2016
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1495.html

Citation Data

DOI : 10.24350/CIRM.V.19044203
Cite this video as: Diekmann, Odo (2016). Boosting and waning: on the dynamics of immune status. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19044203
URI : http://dx.doi.org/10.24350/CIRM.V.19044203

Voir aussi


  • [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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