General epidemiological models: Law of large numbers and contact tracing

Duchamps, Jean-Jil; Foutel-Rodier, Félix; Schertzer, Emmanuel

doi:10.48550/arxiv.2106.13135

Cited by 1 publication

(3 citation statements)

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“…Then, up to the choice of the initial condition and the fact that we make a branching assumption, the model considered in Forien et al (2021a) coincides with the model considered here for this specific choice of the pair (P, X ). (It coincides exactly with the extension of our model considered in Duchamps et al (2021). )…”

Section: Relation With Previous Work and Outlinesupporting

confidence: 89%

“…Finally, as far as we can tell, the duality result exposed in Section 2.4 is new and can presumably be extended to more general branching processes where birth and death rates are allowed to be frequency-dependent. In Duchamps et al (2021), some of the authors of the present work show that this duality result has a natural counterpart in a model with a finite but large population.…”

Section: Relation With Previous Work and Outlinesupporting

confidence: 53%

“…(This branching hypothesis is relaxed in a recent work by some of the authors, see Duchamps et al (2021)).…”

Section: Generic Stochastic Model Assumptionsmentioning

confidence: 97%

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From individual-based epidemic models to McKendrick-von Foerster PDEs: a guide to modeling and inferring COVID-19 dynamics

et al. 2022

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We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual’s infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.

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Section: Relation With Previous Work and Outlinesupporting

confidence: 89%

Section: Relation With Previous Work and Outlinesupporting

confidence: 53%