Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19
This article has been Reviewed by the following groups
Discuss this preprint
Start a discussion What are Sciety discussions?Listed in
- Evaluated articles (ScreenIT)
Abstract
Hawkes processes are a form of self-exciting process that has been used in numerous applications, including neuroscience, seismology, and terrorism. While these self-exciting processes have a simple formulation, they can model incredibly complex phenomena. Traditionally Hawkes processes are a continuous-time process, however we enable these models to be applied to a wider range of problems by considering a discrete-time variant of Hawkes processes. We illustrate this through the novel coronavirus disease (COVID-19) as a substantive case study. While alternative models, such as compartmental and growth curve models, have been widely applied to the COVID-19 epidemic, the use of discrete-time Hawkes processes allows us to gain alternative insights. This paper evaluates the capability of discrete-time Hawkes processes by modelling daily mortality counts as distinct phases in the COVID-19 outbreak. We first consider the initial stage of exponential growth and the subsequent decline as preventative measures become effective. We then explore subsequent phases with more recent data. Various countries that have been adversely affected by the epidemic are considered, namely, Brazil, China, France, Germany, India, Italy, Spain, Sweden, the United Kingdom and the United States. These countries are all unique concerning the spread of the virus and their corresponding response measures. However, we find that this simple model is useful in accurately capturing the dynamics of the process, despite hidden interactions that are not directly modelled due to their complexity, and differences both within and between countries. The utility of this model is not confined to the current COVID-19 epidemic, rather this model could explain many other complex phenomena. It is of interest to have simple models that adequately describe these complex processes with unknown dynamics. As models become more complex, a simpler representation of the process can be desirable for the sake of parsimony.
Article activity feed
-
-
SciScore for 10.1101/2020.10.28.20221077: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: Thank you for sharing your code and data.
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Despite this model being able to accurately capture the dynamics of this complex process, some limitations and extensions could be considered. As the epidemic is still ongoing, new data is becoming available each day, and the model must be re-fit and re-tuned each time the data is updated. Additional change points can also be considered when there are significant changes in the trend, such as second waves of infection. An algorithm …
SciScore for 10.1101/2020.10.28.20221077: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: Thank you for sharing your code and data.
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:Despite this model being able to accurately capture the dynamics of this complex process, some limitations and extensions could be considered. As the epidemic is still ongoing, new data is becoming available each day, and the model must be re-fit and re-tuned each time the data is updated. Additional change points can also be considered when there are significant changes in the trend, such as second waves of infection. An algorithm with automatic selection of the number of change points and their respective locations could also be considered. However, additional change points need to be determined carefully as the length of time between each change point must be sufficient. Another consideration is a Bayesian nonparametric spline [57], providing time-varying parameters through flexible splines. However, the identifiability and existence of this model would need to be established. One could also consider different triggering kernels, including nonparametric kernels in order to improve the flexibility of the model. Our model considers only the infected population, as opposed to standard epidemiological models that differentiate the population into several groups depending on their infection status, for example, the SIR model. It is helpful to consider a stochastic variation of the SIR model as a bivariate Poisson process, comprised of infection and recovery events, to compare the two frameworks. Infection events are then governed by a Poisson process where the rate is based on ...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
- No protocol registration statement was detected.
-
