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scientific article; zbMATH DE number 7709547

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English	No label defined	scientific article; zbMATH DE number 7709547

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scholarly article

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Raphaël Forien

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Etienne Pardoux

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publication date

10 July 2023

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full work available at URL

https://arxiv.org/abs/2106.08466

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https://gradmath.org/2023/01/12/recent-advances-in-epidemic-modeling-non-markov-stochastic-models-and-their-scaling-limits/

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zbMATH Keywords

non-Markov epidemic models

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integral equations

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partial differential equations

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varying infectivity

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varying susceptiblity/immunity

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MaRDI profile type

MaRDI publication profile

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An optimal isolation policy for an epidemic

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Optimal immunisation policies for epidemics

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Asymptotic Profiles of the Steady States for an SIS Epidemic Patch Model

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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model

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Limit theorems for a random graph epidemic model

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Finite state graphon games with applications to epidemics

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Optimal Incentives to Mitigate Epidemics: A Stackelberg Mean Field Game Approach

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A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models

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The final size and severity of a generalised stochastic multitype epidemic model

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Network epidemic models with two levels of mixing

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Chapter 1 Single Population Epidemics

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Epidemics on random intersection graphs

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On a functional central limit theorem for Markov population processes

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The duration of the closed stochastic epidemic

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Multi-patch and multi-group epidemic models: a new framework

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SIS epidemic propagation on hypergraphs

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Optimal control of epidemic size and duration with limited resources

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React or wait: which optimal culling strategy to control infectious diseases in wildlife

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Diffusion approximation for an age-structured population

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On a Nonlinear Integral Equation for Population Growth Problems

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Mathematical Models in Epidemiology

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A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2

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Chapter 1 Stochastic Epidemic Models

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Volterra Integral Equations

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SIR epidemic models with general infectious period distribution

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A stochastic SIR model with contact-tracing: large population limits and statistical inference

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An epidemic equation with immigration

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A general-age-dependent branching process. II

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A general age-dependent branching process. I

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Large graph limit for an SIR process in random network with heterogeneous connectivity

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Limiting behaviour in an epidemic model

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Contact rate epidemic control of COVID-19: an equilibrium view

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Epidemiological models with non-exponentially distributed disease stages and applications to disease control

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Epidemic Models with Varying Infectivity

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Household epidemic models and McKean-Vlasov Poisson driven stochastic differential equations

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SIR epidemics and vaccination on random graphs with clustering

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Random Perturbations of Dynamical Systems

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

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On SIR epidemic models with generally distributed infectious periods: Number of secondary cases and probability of infection

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Optimal control of epidemics with limited resources

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An SIS epidemic model with variable population size and a delay

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An age dependent epidemic model

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Incentives, lockdown, and testing: from Thucydides' analysis to the COVID-19 pandemic

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On the dynamics of a class of multi-group models for vector-borne diseases

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Kermack and McKendrick revisited: The variable subsceptibility model for infectious deseases

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A mathematical model for Chagas disease with infection-age-dependent infectivity

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Law of large numbers for the SIR epidemic on a random graph with given degrees

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Near-critical SIR epidemic on a random graph with given degrees

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Local-density dependent Markov processes on graphons with epidemiological applications

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Contributions to the mathematical theory of epidemics. III.—Further studies of the problem of endemicity

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Dynamic games of social distancing during an epidemic: analysis of asymmetric solutions

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Large Deviations for Infectious Diseases Models

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Solutions of ordinary differential equations as limits of pure jump markov processes

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Two-Group Infection Age Model Including an Application to Nosocomial Infection

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Lyapunov functional and global asymptotic stability for an infection-age model

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Final Size of an Epidemic for a Two-Group SIR Model

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Final size of a multi-group SIR epidemic model: irreducible and non-irreducible modes of transmission

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An Introduction to Mathematical Epidemiology

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Slow and fast scales for superprocess limits of age-structured populations

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On the optimal control of a deterministic epidemic

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A SIR model on a refining spatial grid. I: Law of large numbers

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Limit theorems for age-structured populations

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Functional limit theorems for non-Markovian epidemic models

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Probabilistic Models of Population Evolution

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Moderate deviations and extinction of an epidemic

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Large deviation principle for epidemic models

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Large deviation principle for reflected Poisson driven stochastic differential equations in epidemic models

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The Law of Large Numbers for $D[0,1]$-Valued Random Variables

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Central limit theorems for local martingales

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The asymptotic evolution of the general stochastic epidemic

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On the asymptotic distribution of the size of a stochastic epidemic

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How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS?

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Chapter 3 SIR Epidemics on Configuration Model Graphs

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A simple SIS epidemic model with a backward bifurcation

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Critical epidemics, random graphs, and Brownian motion with a parabolic drift

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Limit theorems for age and density dependent stochastic population models

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A central limit theorem for age- and density-dependent population processes

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Gaussian approximation of some closed stochastic epidemic models

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Asymptotic Behavior of Some Deterministic Epidemic Models

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Optimal immunization rules for an epidemic with recovery

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Optimal isolation policies for deterministic and stochastic epidemics

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A SIRS epidemic model with infection-age dependence

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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