English
Boosting and waning: on the dynamics of immune status
Post-edited
Auteurs : Diekmann, Odo (Auteur de la conférence)
CIRM (Editeur )
45D05 - Volterra integral equations
60J75 - Jump processes
92D30 - Epidemiology
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 : 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.
45D05 - Volterra integral equations
60J75 - Jump processes
92D30 - Epidemiology
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 13/09/2016 Date de Captation : 06/09/2016 Collection : Exposés de recherche Sous Collection : Research talks Catégorie arXiv : Quantitative Biology ; Dynamical Systems Domaine(s) : Systèmes Dynamiques & EDO ; Mathématiques pour les Sciences & Technologies Format : MP4 (.mp4) - HD Durée : 00:58:03 Audience : Chercheurs Download : https://videos.cirm-math.fr/2016-09-06_Diekmann.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Models in population dynamics and ecology / Modèles en dynamique des populations et écologieOrganisateurs 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 de la Rencontre : http://conferences.cirm-math.fr/1495.html
Données de citation
DOI : 10.24350/CIRM.V.19044203Citer cette vidéo: 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 |
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Bibliographie
- [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
