Français
Recent results on epidemic models
Multi angle
Authors : Pardoux, Etienne (Author of the conference)
CIRM (Publisher )
60F15 - Strong theorems
60G55 - Point processes
92D30 - Epidemiology
Additional resources :
https://www.cirm-math.fr/RepOrga/2390/Slides/Etienne_Pardoux.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2390/Slides/Etienne_Pardoux.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 27/09/2023 Conference Date : 07/09/2023 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:48:14 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-07_Pardoux.mp4 
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Information on the Event
Event Title : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériquesEvent Organizers : Champagnat, Nicolas ; Pagès, Gilles ; Tanré, Etienne ; Tomašević, Milica Dates : 04/09/2023 - 08/09/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2390.html
Citation Data
DOI : 10.24350/CIRM.V.20088703Cite this video as: 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 |
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Bibliography
- 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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