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Boosting and waning: on the dynamics of immune status
Post-edited
Authors : Diekmann, Odo (Author of the conference)
CIRM (Publisher )
45D05 - Volterra integral equations
60J75 - Jump processes
92D30 - Epidemiology
CIRM (Publisher )
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| model ingredients random variable and kernel renewal equation dynamical system perspective stable distribution travel time Questions of the audience |
Abstract :
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.
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/09/2016 Conference Date : 06/09/2016 Subseries : Research talks arXiv category : Quantitative Biology ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Mathematics in Science & Technology Format : MP4 (.mp4) - HD Video Time : 00:58:03 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-09-06_Diekmann.mp4 
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Information on the Event
Event Title : Models in population dynamics and ecology / Modèles en dynamique des populations et écologieEvent Organizers : Langlais, Michel ; Malchow, Horst ; Petrovskii, Sergei ; Poggiale, Jean-Christophe Dates : 05/09/2016 - 09/09/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1495.html
Citation Data
DOI : 10.24350/CIRM.V.19044203Cite 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 |
See Also
- [Multi angle] About mathematical modelling for microbial ecosystems with control and design perspectives / Author of the conference Rapaport, Alain.
- [Multi angle] Challenges in the management of ecological populations / Author of the conference Hastings, Alan.
- [Multi angle] Catching ghosts with a coarse net: real and imaginary effects in ecological monitoring routine based on sparse sampling / Author of the conference Petrovskaya, Natalia.
- [Multi angle] Evolutionary branching: trade-offs and magic traits / Author of the conference Kisdi, Eva.
Bibliography
- [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
