scholarly journals A Hawkes process model for the propagation of COVID-19: simple analytical results

2021 ◽  
Author(s):  
Juan Valentin Escobar
Keyword(s):  
Clinical Trials ◽  
Exponential Function ◽  
Process Model ◽  
Branching Process ◽  
Hawkes Process ◽  
Memory Kernel ◽  
Analytical Results ◽  
Analytical Expressions

Abstract We present a model for the COVID-19 epidemic that offers analytical expressions for the newly registered and latent cases. This model is based on an epidemic branching process with latency that is greatly simplified when the bare memory kernel is given by an exponential function as observed in this pandemic. We expose the futility of the concept of “bending the curve” of the epidemic as long as the number of latent cases is not depleted. Our model offers the possibility of laying out different scenarios for the evolution of the epidemic in different countries based on the most recent observations and in terms of only two constants obtained from clinical trials.

scholarly journals A Hawkes process model for the propagation of COVID-19: simple analytical results

2020 ◽  
Author(s):  
Juan Valentin Escobar
Keyword(s):  
Clinical Trials ◽  
Exponential Function ◽  
Process Model ◽  
Branching Process ◽  
Hawkes Process ◽  
Memory Kernel ◽  
Analytical Results ◽  
The Usa ◽  
Analytical Expressions

Abstract We present a model for the COVID-19 epidemic that offers analytical expressions for the newly registered and latent cases. This model is based on an epidemic branching process with latency that is greatly simplified when the bare memory kernel is given by an exponential function as observed in this pandemic. We expose the futility of the concept of “reaching the peak” of the epidemic as long as the number of latent cases is not depleted. Our model offers the possibility of laying out different scenarios for the evolution of the epidemic in different countries based on the most recent observations and in terms of only two constants obtained from clinical trials. Furthermore, by analyzing the number of registered new deaths, our model suggests that the recent surge in new COVID-19 cases in the USA is a consequence of an increase in testing, but only up to the second week of June of 2020.

scholarly journals The Probability of Fixation in Populations of Changing Size

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 723-733 ◽  
Author(s):  
Sarah P Otto ◽  
Michael C Whitlock
Keyword(s):  
Diffusion Equation ◽  
Adaptive Evolution ◽  
Process Model ◽  
Branching Process ◽  
Approximate Solutions ◽  
Logistic Growth ◽  
Beneficial Mutations ◽  
Demographic Models ◽  
Deleterious Alleles ◽  
Probability Of Fixation

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

scholarly journals Predicting Water Pipe Failures with a Recurrent Neural Hawkes Process Model

2020 ◽  
Author(s):  
Jeroen Verheugd ◽  
Paulo R de Oliveira da Costa ◽  
Reza Refaei Afshar ◽  
Yingqian Zhang ◽  
Sjoerd Boersma
Keyword(s):  
Process Model ◽  
Hawkes Process ◽  
Water Pipe

scholarly journals A branching process model for the analysis of abortive colony size distributions in carbon ion-irradiated normal human fibroblasts

2014 ◽  
Vol 55 (3) ◽  
pp. 423-431 ◽  
Author(s):  
T. Sakashita ◽  
N. Hamada ◽  
I. Kawaguchi ◽  
T. Hara ◽  
Y. Kobayashi ◽  
...  
Keyword(s):  
Colony Size ◽  
Process Model ◽  
Branching Process ◽  
Human Fibroblasts ◽  
Size Distributions ◽  
Carbon Ion ◽  
Normal Human

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

scholarly journals Simulating the impact of vaccination rates on the initial stages of a COVID-19 outbreak in New Zealand (Aotearoa) with a stochastic model

2021 ◽  
Author(s):  
Leighton M Watson
Keyword(s):  
New Zealand ◽  
Stochastic Model ◽  
Process Model ◽  
Branching Process ◽  
Total Population ◽  
Median Number ◽  
Vaccination Rate ◽  
Vaccination Rates ◽  
The Impact ◽  
Different Levels

Aim: The August 2021 COVID-19 outbreak in Auckland has caused the New Zealand government to transition from an elimination strategy to suppression, which relies heavily on high vaccination rates in the population. As restrictions are eased and as COVID-19 leaks through the Auckland boundary, there is a need to understand how different levels of vaccination will impact the initial stages of COVID-19 outbreaks that are seeded around the country. Method: A stochastic branching process model is used to simulate the initial spread of a COVID-19 outbreak for different vaccination rates. Results: High vaccination rates are effective at minimizing the number of infections and hospitalizations. Increasing vaccination rates from 20% (approximate value at the start of the August 2021 outbreak) to 80% (approximate proposed target) of the total population can reduce the median number of infections that occur within the first four weeks of an outbreak from 1011 to 14 (25th and 75th quantiles of 545-1602 and 2-32 for V=20% and V=80%, respectively). As the vaccination rate increases, the number of breakthrough infections (infections in fully vaccinated individuals) and hospitalizations of vaccinated individuals increases. Unvaccinated individuals, however, are 3.3x more likely to be infected with COVID-19 and 25x more likely to be hospitalized. Conclusion: This work demonstrates the importance of vaccination in protecting individuals from COVID-19, preventing high caseloads, and minimizing the number of hospitalizations and hence limiting the pressure on the healthcare system.

Multivariate Hawkes process model of market participants behavior in the high frequency world

2021 ◽  
Vol 08 (01) ◽  
pp. 2050054
Author(s):  
Sugato Chakravarty ◽  
Kiseop Lee ◽  
Yang Xi
Keyword(s):  
Public Sector ◽  
High Frequency ◽  
Process Model ◽  
Hawkes Process ◽  
Transaction Data ◽  
The Public ◽  
Market Participants ◽  
Public Sector Banks ◽  
Average Return ◽  
Causality Relationship

We propose a multivariate Hawkes process to model the interaction between the non-high frequency traders (NHFTs) behavior (Buy and sell) and high frequency traders (HFTs) behavior (Buy and sell). We apply our model to the intraday transaction data of the public sector banks stock in India, which is sampled from March 2012 to June 2012. We find that the mutually-exciting NHFT and HFT behaviors benefit the stocks, which have better average return above the average return of the public sector bank index. We further identify the granger causality relationship for mutually exciting dominating stocks that HFTs activities cause the activities of NHFTs. In other words, NHFTs are market followers in those stocks.

scholarly journals Cancer recurrence times from a branching process model

2019 ◽  
Vol 15 (11) ◽  
pp. e1007423 ◽  
Author(s):  
Stefano Avanzini ◽  
Tibor Antal
Keyword(s):  
Process Model ◽  
Branching Process ◽  
Cancer Recurrence ◽  
Recurrence Times
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