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  1. Book ; Online: Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection

    Favero, Martina / Jenkins, Paul A.

    2023  

    Abstract: Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling ... ...

    Abstract Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. Under a finite-allele mutation model, with possibly parent-dependent mutation, we consider the asymptotic regime where the selective advantage of one allele grows to infinity, while the other parameters remain fixed. In this regime, we show that the Wright-Fisher diffusion can be approximated either by a Gaussian process or by a process whose components are independent continuous-state branching processes with immigration, aligning with analogous results for Wright-Fisher models but employing different methods. While the first process becomes degenerate at stationarity, the latter does not and provides a simple, analytic approximation for the leading term of the sampling probability. Furthermore, using another approach based on a recursion formula, we characterise all remaining terms to provide a full asymptotic expansion for the sampling probability. Finally, we study the asymptotic behaviour of the rates of the block-counting process of the conditional ancestral selection graph and establish an asymptotic duality relationship between this and the diffusion.

    Comment: 41 pages
    Keywords Mathematics - Probability ; Quantitative Biology - Populations and Evolution
    Subject code 519
    Publishing date 2023-12-28
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article ; Online: Modelling preventive measures and their effect on generation times in emerging epidemics.

    Favero, Martina / Scalia Tomba, Gianpaolo / Britton, Tom

    Journal of the Royal Society, Interface

    2022  Volume 19, Issue 191, Page(s) 20220128

    Abstract: We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing ... ...

    Abstract We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.
    MeSH term(s) COVID-19/epidemiology ; COVID-19/prevention & control ; Contact Tracing/methods ; Disease Outbreaks/prevention & control ; Epidemics/prevention & control ; Humans
    Language English
    Publishing date 2022-06-15
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2156283-0
    ISSN 1742-5662 ; 1742-5689
    ISSN (online) 1742-5662
    ISSN 1742-5689
    DOI 10.1098/rsif.2022.0128
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  3. Article ; Online: A dual process for the coupled Wright-Fisher diffusion.

    Favero, Martina / Hult, Henrik / Koski, Timo

    Journal of mathematical biology

    2021  Volume 82, Issue 1-2, Page(s) 6

    Abstract: The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, ... ...

    Abstract The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, an ancestral process, which is dual to the coupled Wright-Fisher diffusion, is derived. The dual process corresponds to the block counting process of coupled ancestral selection graphs, one for each locus. Jumps of the dual process arise from coalescence, mutation, single-branching, which occur at one locus at the time, and double-branching, which occur simultaneously at two loci. The coalescence and mutation rates have the typical structure of the transition rates of the Kingman coalescent process. The single-branching rate not only contains the one-locus selection parameters in a form that generalises the rates of an ancestral selection graph, but it also contains the two-locus selection parameters to include the effect of the pairwise interaction on the single loci. The double-branching rate reflects the particular structure of pairwise selection interactions of the coupled Wright-Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright-Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.
    MeSH term(s) Alleles ; Gene Frequency ; Genetics, Population ; Models, Genetic ; Mutation ; Mutation Rate ; Selection, Genetic
    Language English
    Publishing date 2021-01-22
    Publishing country Germany
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 187101-8
    ISSN 1432-1416 ; 0303-6812
    ISSN (online) 1432-1416
    ISSN 0303-6812
    DOI 10.1007/s00285-021-01555-9
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  4. Book ; Online: Modelling preventive measures and their effect on generation times in emerging epidemics

    Favero, Martina / Tomba, Gianpaolo Scalia / Britton, Tom

    2022  

    Abstract: We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing ... ...

    Abstract We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.

    Comment: 26 pages, 4 figures, 5 tables
    Keywords Quantitative Biology - Populations and Evolution ; Mathematics - Probability ; Statistics - Applications
    Subject code 612
    Publishing date 2022-01-24
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article: Estimates of the proportion of SARS-CoV-2 infected individuals in Sweden

    Hult, Henrik / Favero, Martina

    Abstract: In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsible for COVID-19. To capture heterogeneity in the population and the effect of interventions to reduce the rate of ... ...

    Abstract In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsible for COVID-19. To capture heterogeneity in the population and the effect of interventions to reduce the rate of epidemic spread, the model uses a time-varying contact rate, whose logarithm has a Gaussian process prior. A Poisson point process is used to model the occurrence of deaths due to COVID-19 and the model is calibrated using data of daily death counts in combination with a snapshot of the the proportion of individuals with an active infection, performed in Stockholm in late March. The methodology is applied to regions in Sweden. The results show that the estimated proportion of the population who has been infected is around 13.5% in Stockholm, by 2020-05-15, and ranges between 2.5% - 15.6% in the other investigated regions. In Stockholm where the peak of daily death counts is likely behind us, parameter uncertainty does not heavily influence the expected daily number of deaths, nor the expected cumulative number of deaths. It does, however, impact the estimated cumulative number of infected individuals. In the other regions, where random sampling of the number of active infections is not available, parameter sharing is used to improve estimates, but the parameter uncertainty remains substantial.
    Keywords covid19
    Publisher ArXiv
    Document type Article
    Database COVID19

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  6. Book ; Online: Estimates of the proportion of SARS-CoV-2 infected individuals in Sweden

    Hult, Henrik / Favero, Martina

    2020  

    Abstract: In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsible for COVID-19. To capture heterogeneity in the population and the effect of interventions to reduce the rate of ... ...

    Abstract In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsible for COVID-19. To capture heterogeneity in the population and the effect of interventions to reduce the rate of epidemic spread, the model uses a time-varying contact rate, whose logarithm has a Gaussian process prior. A Poisson point process is used to model the occurrence of deaths due to COVID-19 and the model is calibrated using data of daily death counts in combination with a snapshot of the the proportion of individuals with an active infection, performed in Stockholm in late March. The methodology is applied to regions in Sweden. The results show that the estimated proportion of the population who has been infected is around 13.5% in Stockholm, by 2020-05-15, and ranges between 2.5% - 15.6% in the other investigated regions. In Stockholm where the peak of daily death counts is likely behind us, parameter uncertainty does not heavily influence the expected daily number of deaths, nor the expected cumulative number of deaths. It does, however, impact the estimated cumulative number of infected individuals. In the other regions, where random sampling of the number of active infections is not available, parameter sharing is used to improve estimates, but the parameter uncertainty remains substantial.
    Keywords Quantitative Biology - Populations and Evolution ; Physics - Physics and Society ; 62P10 ; covid19
    Subject code 310
    Publishing date 2020-05-25
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Book ; Online: Estimates of the proportino of SARS-CoV-2 infected individuals in Sweden

    Hult, Henrik / Favero, Martina

    Abstract: In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsi- ble for COVID-19. To capture heterogeneity in the population and the eect of interventions to reduce the rate of ... ...

    Abstract In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsi- ble for COVID-19. To capture heterogeneity in the population and the eect of interventions to reduce the rate of epidemic spread, the model uses a time- varying contact rate, whose logarithm has a Gaussian process prior. A Poisson point process is used to model the occurrence of deaths due to COVID-19 and the model is calibrated using data of daily death counts in combination with a snapshot of the the proportion of individuals with an active infection, per- formed in Stockholm in late March. The methodology is applied to regions in Sweden. The results show that the estimated proportion of the population who has been infected is around 13:5% in Stockholm, by 2020-05-15, and ranges be- tween 2.5%-15.6% in the other investigated regions. In Stockholm where the peak of daily death counts is likely behind us, parameter uncertainty does not heavily inuence the expected daily number of deaths, nor the expected cumu- lative number of deaths. It does, however, impact the estimated cumulative number of infected individuals. In the other regions, where random sampling of the number of active infections is not available, parameter sharing is used to improve estimates, but the parameter uncertainty remains substantial.

    QC 20200527
    Keywords Epidemic model ; COVID-19 ; SARS-CoV-2 ; Probability Theory and Statistics ; Sannolikhetsteori och statistik ; covid19
    Subject code 310
    Language English
    Publisher KTH, Matematisk statistik
    Publishing country se
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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