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Browning R, Sulem D, Mengersen K, et al. Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19. PLoS One. 2021;16(4):e0250015doi: 10.1371/journal.pone.0250015.
Browning, R., Sulem, D., Mengersen, K., Rivoirard, V., & Rousseau, J. (2021). Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19. PloS one, 16(4), e0250015. https://doi.org/10.1371/journal.pone.0250015
Browning, Raiha, et al. "Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19." PloS one vol. 16,4 (2021): e0250015. doi: https://doi.org/10.1371/journal.pone.0250015
Browning R, Sulem D, Mengersen K, Rivoirard V, Rousseau J. Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19. PLoS One. 2021 Apr 09;16(4):e0250015. doi: 10.1371/journal.pone.0250015. eCollection 2021. PMID: 33836020; PMCID: PMC8034752.
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PLoS One. 2021 Apr 09;16(4):e0250015. doi: 10.1371/journal.pone.0250015. eCollection 2021.

Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19.

PloS one

Raiha Browning, Deborah Sulem, Kerrie Mengersen, Vincent Rivoirard, Judith Rousseau

Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
  2. Australian Research Council, Centre of Excellence for Mathematical and Statistical Frontiers, Brisbane, Australia.
  3. Department of Statistics, University of Oxford, Oxford, United Kingdom.
  4. Ceremade, Université Paris-Dauphine, Paris, France.

PMID: 33836020 PMCID: PMC8034752 DOI: 10.1371/journal.pone.0250015

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.

Conflict of interest statement

The authors have declared that no competing interests exist.

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