English
Recent results on epidemic models
Multi angle
Auteurs : Pardoux, Etienne (Auteur de la Conférence)
CIRM (Editeur )
60F15 - Strong theorems
60G55 - Point processes
92D30 - Epidemiology
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2390/Slides/Etienne_Pardoux.pdf
CIRM (Editeur )
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Résumé :
In 1927, two Scottish epidemiologists, Kermack and McKendrick, published a paper on a SIR epidemic model, where each infectious individual has an age of infection dependent infectivity, and a random infectious period whose law is very general. This paper was quoted a huge number of times, but almost all authors who quoted it considered the simple case of a constant infectivity, and a duration of infection following the exponential distribution, in which case the integral equation model of Kermack and McKendrick reduces to an ODE.
It is classical that an ODE epidemic model is the Law of Large Numbers limits, as the size of the population tends to infinity, of finite population stochastic Markovian epidemic models.
One of our main contributions in recent years has been to show that the integral equation epidemic model of Kermack and McKendrick is the law of large numbers limit of stochastic non Markovian epidemic models. It is not surprising that the model of Kermack and Mc Kendrick, unlike ODE models, has a memory, like non Markovian stochastic processes. One can also write the model as a PDE, where the additional variable is the age of infection of each infected individual.
Similar PDE models have been introduced by Kermack and Mc Kendrick in their 1932 and 1933 papers, where they add a progressive loss of immunity. We have also shown that this 1932-33 model is the Law of Large Numbers limit of appropriate finite population non Markovian models.
Joint work with R. Forien (INRAE Avignon, France), G. Pang (Rice Univ., Houston, Texas, USA) and A.B. Zotsa-Ngoufack (AMU and Univ. Yaoundé 1)
Keywords : Varying infectivity; waning immunity; epidemic models with memory
Codes MSC : It is classical that an ODE epidemic model is the Law of Large Numbers limits, as the size of the population tends to infinity, of finite population stochastic Markovian epidemic models.
One of our main contributions in recent years has been to show that the integral equation epidemic model of Kermack and McKendrick is the law of large numbers limit of stochastic non Markovian epidemic models. It is not surprising that the model of Kermack and Mc Kendrick, unlike ODE models, has a memory, like non Markovian stochastic processes. One can also write the model as a PDE, where the additional variable is the age of infection of each infected individual.
Similar PDE models have been introduced by Kermack and Mc Kendrick in their 1932 and 1933 papers, where they add a progressive loss of immunity. We have also shown that this 1932-33 model is the Law of Large Numbers limit of appropriate finite population non Markovian models.
Joint work with R. Forien (INRAE Avignon, France), G. Pang (Rice Univ., Houston, Texas, USA) and A.B. Zotsa-Ngoufack (AMU and Univ. Yaoundé 1)
Keywords : Varying infectivity; waning immunity; epidemic models with memory
60F15 - Strong theorems
60G55 - Point processes
92D30 - Epidemiology
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2390/Slides/Etienne_Pardoux.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 27/09/2023 Date de captation : 07/09/2023 Sous collection : Research talks arXiv category : Probability Domaine : Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:48:14 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-07_Pardoux.mp4 
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Informations sur la Rencontre
Nom de la rencontre : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériquesOrganisateurs de la rencontre : Champagnat, Nicolas ; Pagès, Gilles ; Tanré, Etienne ; Tomašević, Milica Dates : 04/09/2023 - 08/09/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2390.html
Données de citation
DOI : 10.24350/CIRM.V.20088703Citer cette vidéo: Pardoux, Etienne (2023). Recent results on epidemic models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20088703 URI : http://dx.doi.org/10.24350/CIRM.V.20088703 |
Voir aussi
- [Multi angle] Two examples of thermodynamic limits in neuroscience / Auteur de la Conférence Faugeras, Olivier.
- [Multi angle] Conditional propagation of chaos for generalized Hawkes processes having alpha-stable jump heights / Auteur de la Conférence Löcherbach, Eva.
- [Multi angle] Rearranged stochastic heat equation / Auteur de la Conférence Delarue, François.
- [Multi angle] Functional convex order for stochastic processes: a constructive (and simulable) approach / Auteur de la Conférence Pagès, Gilles.
- [Multi angle] Optimal revelated utilities and convex pricing kernels: - a forward point of view of convexity propagation / Auteur de la Conférence El Karoui, Nicole.
- [Multi angle] Stochastic control for medical treatment optimization / Auteur de la Conférence de Saporta, Benoîte.
- [Multi angle] Systematic jump risk / Auteur de la Conférence Jacod, Jean.
- [Multi angle] Propagation of chaos for stochastic particle systems with singular mean-field interaction of $L^{q}-L^{p}$ type / Auteur de la Conférence Tomašević, Milica.
- [Multi angle] Construction of Boltzmann and McKean Vlasov type flows (the sewing lemma approach) / Auteur de la Conférence Bally, Vlad.
- [Multi angle] Wasserstein convergence of penalized Markov processes / Auteur de la Conférence Champagnat, Nicolas.
- [Multi angle] Exponent dynamics for branching processes / Auteur de la Conférence Méléard, Sylvie.
- [Multi angle] Gambling for resurrection and the heat equation on a triangle / Auteur de la Conférence Blanchet-Scalliet, Christophette.
- [Multi angle] Cox Construction: a random walk in the land of stochastic analysis and numerical probability / Auteur de la Conférence Protter, Philip.
- [Multi angle] Large random matrices and PDE's / Auteur de la Conférence Lions, Pierre-Louis.
Bibliographie
- R. Forien, G. Pang and É Pardoux, Estimating the state of the Covid-19 epidemic in France using a non-Markov model, Royal Soc. Open Science 8, 202327, 2021. - https://doi.org/10.1098/rsos.202327
- R. Forien, G. Pang and É Pardoux, Epidemic models with varying infectivity, SIAM J. Applied Math. 81, 1893-1930, 2021. - https://doi.org/10.1137/20M1353976
- R. Forien, G. Pang and É Pardoux, Multi-patch multi-group epidemic model with with varying infectivity, Probability, Uncertainty and Quantitative Risk 7, 333-364, 2022. - https://doi.org/10.3934/puqr.2022019
- R. Forien, G. Pang and É Pardoux, Recent advances in epidemic modeling: non Markov stochastic models and their scaling limits, Graduate J. Math. 7, 19-75, 2022. - https://doi.org/10.48550/arXiv.2106.08466
- G. Pang and É Pardoux, Functional law of large numbers and PDEs for epidemic models with infection age dependent infectivity, Applied Math & Optimization 87, 2023. - https://doi.org/10.1007/s00245-022-09963-z
- R. Forien, G. Pang, É Pardoux and A.B. Zotsa-Ngoufack, Stochastic epidemic models with varying infectivity and susceptibility, submitted. - https://doi.org/10.48550/arXiv.2210.0466
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