Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area

Gaubert, Stéphane; Akian, Marianne; Allamigeon, Xavier; Boyet, Marin; Colin, Baptiste; Grohens, Théotime; Massoulié, Laurent; Parsons, David; Adnet, Frédéric; Chanzy, Érick; Goix, Laurent; Lapostolle, Frédéric; Lecarpentier, Éric; Leroy, C.; Loeb, Thomas; Marx, J.-S.; Télion, C.; Treluyer, Laurent; Carli, Pierre

doi:10.5802/crmath.99

Cited by 12 publications

(13 citation statements)

References 32 publications

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“…removed) also depends on the time since infection. The results of the present paper are comparable to those in [GAA + 20], where the analysis and the treated data concern the various départements of Î le de France, while we compare Î le de France, the North–East of France, and the rest of the country.…”

Section: Introductionsupporting

confidence: 86%

“…γ ) is the parameter of the exponential law of ε (resp. ℐ), i.e., 𝔼( ε ) = ν −1 , 𝔼(ℐ) γ −1 Note that in the Markovian case, the convergence as N → ∞ is a classical result, see, e.g., [BP19] for a recent account.The above ODE model is the one which is used by almost all papers dealing with epidemic models, in particular the Covid–19 models, with the exception, to our knowledge, of [FKK20], where the case of fixed ε and ℐ is considered and [GAA + 20, SRE + 20]. It is fair to say that the exponential distributions are very poor models for the laws of ε and ℐ, and it may seem strange that the above ODE model is so widely used, while it is based on unrealistic assumptions.…”

Section: Methodsmentioning

confidence: 99%

“…In [FKK20], the authors use ODEs with delays, which correspond to our model with deterministic exposed and infectious periods. On the other hand [GAA + 20], following the approach initiated by Kermack and McKendrick to analyze the plague epidemic in Mumbai in 1905–6 [KM27], uses a transport PDE SEIR model, where the rate of infection by an infectious individual depends upon the time since infection, and the rate at which exposed (resp. infectious) individuals become infectious (resp.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the state of the Covid-19 epidemic in France using a non-Markovian model

Forien

Pang

Pardoux

2020

Preprint

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In this paper, we use a deterministic non-Markovian epidemic model to estimate the state of the Covid-19 epidemic in France. This model allows us to consider realistic distributions for the exposed and infectious periods in a SEIR model, contrary to standard ODE models which only consider exponentially distributed exposed and infectious periods. We present theoretical results linking the (unobserved) parameters of the model to various quantities which are more easily measured during the early stages of an epidemic. We also stress the main quantitative differences between the non-Markovian and the Markovian (ODE) model. We then apply these results to estimate the state of the Covid-19 epidemic in France by analyzing three regions: the Paris region, the northeast regions and the rest of the country, based on current knowledge on the infection fatality ratio and the exposed and infectious periods distributions for Covid-19. Our analysis is based on the hospital data published daily by Santé Publique France (daily hospital admissions, intensive care unit admissions and hospital deaths).

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Section: Introductionsupporting

confidence: 86%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating the state of the Covid-19 epidemic in France using a non-Markovian model

Forien

Pang

Pardoux

2020

Preprint

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“…[4] for a recent account. The above ODE model is the one which is used by almost all papers dealing with epidemic models, in particular the COVID-19 models, with the exception, to our knowledge, of [6], where the case of fixed E and I is considered and [5,8,9]. It is fair to say that the exponential distributions are very poor models for the laws of E and I, and it may seem strange that the above ODE model is so widely used, while it is based on such unrealistic assumptions.…”

Section: Methodsmentioning

confidence: 99%

“…In [ 6 ], the authors use ODEs with delays, which correspond to our model with deterministic exposed and infectious periods. On the other hand, following the approach initiated by Kermack and McKendrick to analyse the plague epidemic in Mumbai in 1905–1906 [ 7 ], [ 8 ] uses a transport PDE SEIR model, where the rate of infection by an infectious individual depends upon the time since infection, and the rate at which exposed (respectively, infectious) individuals become infectious (respectively, removed) also depends on the time since infection. The results of the present paper are comparable to those in [ 8 ], where the analysis and the treated data concern the various départements of Île-de-France, while we compare Île-de-France, Grand Est, Provence–Alpes–Côte d’Azur and Auvergne–Rhône–Alpes.…”

Section: Introductionmentioning

confidence: 99%

Estimating the state of the COVID-19 epidemic in France using a model with memory

2021

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In this paper, we use a deterministic epidemic model with memory to estimate the state of the COVID-19 epidemic in France, from early March until mid-December 2020. Our model is in the SEIR class, which means that when a susceptible individual (S) becomes infected, he/she is first exposed (E), i.e. not yet contagious. Then he/she becomes infectious (I) for a certain length of time, during which he/she may infect susceptible individuals around him/her, and finally becomes removed (R), that is, either immune or dead. The specificity of our model is that it assumes a very general probability distribution for the pair of exposed and infectious periods. The law of large numbers limit of such a model is a model with memory (the future evolution of the model depends not only upon its present state, but also upon its past). We present theoretical results linking the (unobserved) parameters of the model to various quantities which are more easily measured during the early stages of an epidemic. We then apply these results to estimate the state of the COVID-19 epidemic in France, using available information on the infection fatality ratio and on the distribution of the exposed and infectious periods. Using the hospital data published daily by Santé Publique France, we gather some information on the delay between infection and hospital admission, intensive care unit (ICU) admission and hospital deaths, and on the proportion of people who have been infected up to the end of 2020.

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Functional Law of Large Numbers and PDEs for Epidemic Models with Infection-Age Dependent Infectivity

Pang

Pardoux

2023

Appl Math Optim

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We study an individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity. Each individual is associated with a random infectivity function, which depends on the age of infection. Individuals are infected through interactions across the locations with heterogeneous effects. The epidemic dynamics in each location is described by the total force of infection, the number of susceptible individuals, the number of infected individuals that are infected at each time and have been infected for a certain amount of time, as well as the number of recovered individuals. The processes can be described using a time-space representation. We prove a functional law of large numbers for these time-space processes, and in the limit, we obtain a set of time-space integral equations. We then derive the PDE models from the limiting time-space integral equations, in particular, the density (with respect to the infection age) of the time-age-space integral equation for the number of infected individuals tracking the age of infection satisfies a linear PDE in time and age with an integral boundary condition. These integral equation and PDE limits can be regarded as dynamics on graphons under certain conditions.

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Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area

Cited by 12 publications

References 32 publications

Estimating the state of the Covid-19 epidemic in France using a non-Markovian model

Estimating the state of the Covid-19 epidemic in France using a non-Markovian model

Estimating the state of the COVID-19 epidemic in France using a model with memory

Functional Law of Large Numbers and PDEs for Epidemic Models with Infection-Age Dependent Infectivity

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