In this paper, we use a deterministic epidemic model with memory to estimate the state of COVID-19 in France, from early March until mid-December 2020. Our is SEIR class, which means that when susceptible individual (S) becomes infected, he/she first exposed (E), i.e. not yet contagious. Then infectious (I) for certain length time, during may infect individuals around him/her, and finally removed (R), is, either immune or dead. The specificity our it assumes very general probability...

In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work the first author, in which information was obtained from forwards-in-time dynamics using novel stochastic partial differential equations approach for spatial $\Lambda$-Fleming-Viot models. The latter were introduced Barton, Etheridge and V\'eber as framework to model evolution genetic composition spatially structured population. Reproduction takes...

We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in regime of weak competition, or equivalently large carrying capacity. Individuals reproduce at random times independently each other but die rate which increases the population size. When individuals reproduce, they produce number offspring, drawn according to some probability distribution on natural integers. keep track descendants initial by adding neutral markers individuals, are inherited one's...

The dynamics of a general structured population is modelled using stochastic differential equation (SDE) with an infinite divisibility property. This property allows the to be divided into arbitrary number allelic components, also known as neutral fractions. When demographic noise small, fast-slow principle provides formula for effective size in populations. To illustrate this approach, we revisit several examples from literature, including age-structured models and expansion fronts.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 July 2020Accepted: 17 May 2021Published online: 13 September 2021Keywordsepidemic model, varying infectivity, infection-age-dependent deterministic integral equations, early phase epidemic, basic reproduction number $R_0$, Poisson random measureAMS Subject Headings45D05, 60F17, 60K35Publication DataISSN (print): 0036-1399ISSN (online): 1095-712XPublisher: Society...

We study the evolution of gene frequencies in a population living $\mathbb{R}^d$, modelled by spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge and Veber, 2010 Etheridge, Veber Yu, 2014). suppose that is divided into two genetic types, $a$ $A$, consider proportion which type at each location. If we let both intensity fraction individuals replaced during reproduction events tend to zero, can be rescaled so as converge solution reaction-diffusion equation (typically...

This paper presents a new view of household epidemic models, where we exploit the fact that interaction between households is mean field type. We prove convergence, as number tends to infinity, infectious individuals in uniformly chosen nonlinear Markov process solving McKean–Vlasov Poisson driven stochastic differential equation, well propagation chaos result. also define basic reproduction R∗ and show if R∗>1, then has unique nontrivial ergodic invariant probability measure, whereas R∗≤1,...

Abstract In this paper, we use a deterministic non-Markovian epidemic model to estimate the state of Covid-19 in France. This allows us consider realistic distributions for exposed and infectious periods SEIR model, contrary standard ODE models which only exponentially distributed periods. We present theoretical results linking (unobserved) parameters various quantities are more easily measured during early stages an epidemic. also stress main quantitative differences between Markovian (ODE)...

In this paper, we consider a mathematical model for the evolution of neutral genetic diversity in spatial continuum including mutations, drift and either short range or long dispersal. The is Λ-Fleming-Viot process introduced by Barton, Etheridge Véber, which describes state population at any time measure on Rd×[0,1], where Rd geographical space [0,1] types. both cases (short dispersal), prove functional central limit theorem as density becomes large under some space-time rescaling. We then...

We introduce a modified spatial Λ-Fleming-Viot process to model the ancestry of individuals in population occupying continuous habitat divided into two areas by sharp discontinuity dispersal rate and effective density. derive an analytical formula for expected number shared haplotype segments between depending on their sampling locations. This involves transition density skew diffusion which appears as scaling limit ancestral lineages this model. then show that can be used infer parameters...

We derive a central limit theorem for spatial $\Lambda$-Fleming-Viot model with fluctuating population size. At each reproduction, proportion of the dies and is replaced by not necessarily equal mass new individuals. The depends on local size function thereof. Additionally, as individuals have single parental type, growing size, events become more frequent smaller impact, modelling successful reproduction higher number From we Wright-Mal\'ecot formula quantifying asymptotic probability...

A bstract In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have higher mutation rate. However, standard models of asexual adaptation the ‘replicator-mutator equation’ often neglect this generation-time effect. study, we investigate emergence positive dependence between consequences dependence. We show that it emerges naturally at population scale, based on large limit stochastic...

We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection. In contrast to classical compartment models, after infection, the infectivity is a random function of time elapsed since one's Similarly, recovered gradually some according susceptibility function. large population asymptotic behaviour model, by proving functional law numbers (FLLN) and investigating endemic equilibria properties limit. The limit depends on...

In this survey paper, we review the recent advances in individual based non--Markovian epidemic models. They include models with a constant infectivity rate, varying rate or infection-age dependent infectivity, recovery (or equivalently, general law of infectious period), as well susceptibility/immunity. We focus on scaling limits large population, functional numbers (FLLN) and central limit theorems (FCLT), while moderate deviations for some Markovian are also reviewed. FLLN, set Volterra...

We study a one-dimensional spatial population model where the sizes at each site are chosen according to translation invariant and ergodic distribution uniformly bounded away from 0 infinity. suppose that frequencies of particular genetic type in colonies evolve system interacting diffusions, following stepping stone Kimura. show that, over large temporal scales, this behaves like solution stochastic heat equation with Wright-Fisher noise constant coefficients. These coefficients effective...

In this paper, we consider a mathematical model for the evolution of neutral genetic diversity in spatial continuum including mutations, drift and either short range or long dispersal. The is $ Λ$-Fleming-Viot process introduced by Barton, Etheridge Véber, which describes state population at any time measure on \R^d \times [0,1] $, where geographical space types. both cases (short dispersal), prove functional central limit theorem as density becomes large under some space-time rescaling. We...