The Experts below are selected from a list of 2973 Experts worldwide ranked by ideXlab platform
Nicholas H Ogden - One of the best experts on this subject based on the ideXlab platform.
-
a Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
Royal Society Open Science, 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incor...
-
a Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
medRxiv, 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:Abstract We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral Equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a Renewal Equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed or coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, the interruption of contact tracing may be irreversible and, depending on the overall growth rate and prevalence of the disease, may lead to outbreaks even in cases when the epidemic was initially under control.
-
A Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
'The Royal Society', 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral Equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a Renewal Equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained
Francesca Scarabel - One of the best experts on this subject based on the ideXlab platform.
-
a Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
Royal Society Open Science, 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incor...
-
a Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
medRxiv, 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:Abstract We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral Equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a Renewal Equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed or coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, the interruption of contact tracing may be irreversible and, depending on the overall growth rate and prevalence of the disease, may lead to outbreaks even in cases when the epidemic was initially under control.
-
A Renewal Equation model to assess roles and limitations of contact tracing for disease outbreak control
'The Royal Society', 2021Co-Authors: Francesca Scarabel, Lorenzo Pellis, Nicholas H OgdenAbstract:We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral Equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a Renewal Equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained
Álvaro Mateos González - One of the best experts on this subject based on the ideXlab platform.
-
Quantitative Convergence Towards a Self-Similar Profile in an Age-Structured Renewal Equation for Subdiffusion
Acta Applicandae Mathematicae, 2016Co-Authors: Hugues Berry, Thomas Lepoutre, Álvaro Mateos GonzálezAbstract:Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the subdiffusive continuous-time random walk using age-structured partial differential Equations with age Renewal upon each walker jump, where the age of a walker is the time elapsed since its last jump. In the spatially-homogeneous (zero-dimensional) case, we follow the evolution in time of the age distribution. An approach inspired by relative entropy techniques allows us to obtain quantitative explicit rates for the convergence of the age distribution to a self-similar profile, which corresponds to convergence to a stationary profile for the rescaled variables. An important difficulty arises from the fact that the Equation in self-similar variables is not autonomous and we do not have a specific analytical solution. Therefore, in order to quantify the latter convergence, we estimate attraction to a time-dependent “pseudo-equilibrium”, which in turn converges to the stationary profile.
-
erratum to quantitative convergence towards a self similar profile in an age structured Renewal Equation for subdiffusion
Acta Applicandae Mathematicae, 2016Co-Authors: Hugues Berry, Thomas Lepoutre, Álvaro Mateos GonzálezAbstract:Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the subdiffusive continuous-time random walk using age-structured partial differential Equations with age Renewal upon each walker jump, where the age of a walker is the time elapsed since its last jump. In the spatially-homogeneous (zero-dimensional) case, we follow the evolution in time of the age distribution. An approach inspired by relative entropy techniques allows us to obtain quantitative explicit rates for the convergence of the age distribution to a self-similar profile, which corresponds to convergence to a stationary profile for the rescaled variables. An important difficulty arises from the fact that the Equation in self-similar variables is not autonomous and we do not have a specific analytical solution. Therefore, in order to quantify the latter convergence, we estimate attraction to a time-dependent "pseudo-equilibrium", which in turn converges to the stationary profile.
-
limiting hamilton jacobi Equation for the large scale asymptotics of a subdiffusion jump Renewal Equation
arXiv: Analysis of PDEs, 2016Co-Authors: Vincent Calvez, Pierre Gabriel, Álvaro Mateos GonzálezAbstract:Subdiffusive motion takes place at a much slower timescale than diffusive motion. As a preliminary step to studying reaction-subdiffusion pulled fronts, we consider here the hyperbolic limit $(t,x) \to (t/\varepsilon, x/\varepsilon)$ of an age-structured Equation describing the subdiffusive motion of, e.g., some protein inside a biological cell. Solutions of the rescaled Equations are known to satisfy a Hamilton-Jacobi Equation in the formal limit $\varepsilon \to 0$. In this work we derive uniform Lipschitz estimates, and establish the convergence towards the viscosity solution of the limiting Hamilton-Jacobi Equation. The two main obstacles overcome in this work are the non-existence of an integrable stationary measure, and the importance of memory terms in subdiffusion.
Y Kebir - One of the best experts on this subject based on the ideXlab platform.
-
laplace transforms and the Renewal Equation
Journal of Applied Probability, 1997Co-Authors: Y KebirAbstract:Vinogradov (1973) used the Laplace transform to characterize the IFR class of life distributions and later Block and Savits (1980) extended the characterization to the main reliability classes. Here we use the same transform again to characterize the continuous time Renewal Equation and some properties of its solution.
Gordon E Willmot - One of the best experts on this subject based on the ideXlab platform.
-
on the discounted penalty function in the Renewal risk model with general interclaim times
Insurance Mathematics & Economics, 2007Co-Authors: Gordon E WillmotAbstract:Abstract The defective Renewal Equation satisfied by the Gerber–Shiu discounted penalty function in the Renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. The class of exponential claim size distributions is considered, and the Laplace transform of the (discounted) defective density of the surplus immediately prior to ruin is obtained. The mixed Erlang claim size class is also examined. The simplified defective Renewal Equation which results when the penalty function only involves the deficit is used to obtain moments of the discounted deficit.
-
a generalized defective Renewal Equation for the surplus process perturbed by diffusion
Insurance Mathematics & Economics, 2002Co-Authors: Cary Chiliang Tsai, Gordon E WillmotAbstract:Abstract In this paper, we consider the surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. We generalize the defective Renewal Equation for the expected discounted function of a penalty at the time of ruin in Garber and Landry [Insurance: Math. Econ. 22 (1998) 263]. Then an asymptotic formula for the expected discounted penalty function is proposed. In addition, the associated claim size distribution is studied, and reliability-based class implications for the distribution are given.
-
analysis of a defective Renewal Equation arising in ruin theory
Insurance Mathematics & Economics, 1999Co-Authors: Sheldon X Lin, Gordon E WillmotAbstract:Abstract This paper studies in detail the solution of a defective Renewal Equation which involves the time of ruin, the surplus immediately before ruin, and the deficit at the time of ruin. The analysis is simplified by introduction and analysis of a related compound geometric distribution, which is studied in detail. Tijms approximations and bounds for these quantities are also discussed. Examples are given for the cases when the claim size distribution is exponential, combinations of exponentials and mixtures of Erlangs. In a subsequent paper, we will extend our analysis to the moments of the time of ruin, the moments of the surplus before the time of ruin, the moments of the deficit at the time of ruin, and correlations between them.