![]() Ī Hawkes process is a stochastic, self-exciting process in which past events influence the short-term probability of future events occurring. More detailed approaches such as agent-based modelling have also been considered by numerous authors. Various models based on growth curves have also been proposed, for example, who use logistic, exponential and Richards growth curves respectively. As an alternative to compartmental models, others have used methods such as branching processes to capture the spread of the virus through individual networks, log-linear Poisson autoregressive models, and other probabilistic models of the infection cycle of the virus. A popular choice is compartmental models, with some considering the standard SIR (Susceptible-Infected-Recovered) model, and further extensions in which additional states are introduced. In all of these, statistical and mathematical models are an essential aspect to gaining meaningful insights into how the virus spreads and quantifying its various impacts. There is also a wealth of knowledge around prevention strategies to control the outbreak. There is now an expansive collection of research dedicated to understanding the virus from all perspectives, including its biological, epidemiological, clinical, economic and social impacts. These recommendations are guided by mathematical and statistical modelling to quantify the efficacy of these measures. In the absence of a vaccine, countries implemented a range of non-pharmaceutical interventions and strategies to reduce the spread of the virus, from measures such as social distancing, mask-wearing and contact tracing, to complete city lockdowns and stay at home orders. Since the first reported case in December 2019, countries around the world have fought to contain the virus. It has since spread rapidly with over 116 million confirmed cases and more than 2.5 million deaths as of 7th March 2021. The outbreak of the novel 2019 coronavirus disease (COVID-19) was declared a Global Health Emergency of International Concern on 30th January 2020, and pronounced a Pandemic on 11th March 2020. įunding: The author(s) received no specific funding for this work.Ĭompeting interests: The authors have declared that no competing interests exist. This data was obtained from Johns Hopkins University. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.ĭata Availability: The data used in this analysis are available on Github. Received: NovemAccepted: MaPublished: April 9, 2021Ĭopyright: © 2021 Browning et al. University of Massachusetts, UNITED STATES As models become more complex, a simpler representation of the process can be desirable for the sake of parsimony.Ĭitation: 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. It is of interest to have simple models that adequately describe these complex processes with unknown dynamics. The utility of this model is not confined to the current COVID-19 epidemic, rather this model could explain many other complex phenomena. 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. These countries are all unique concerning the spread of the virus and their corresponding response measures. 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. We then explore subsequent phases with more recent data. We first consider the initial stage of exponential growth and the subsequent decline as preventative measures become effective. ![]() This paper evaluates the capability of discrete-time Hawkes processes by modelling daily mortality counts as distinct phases in the COVID-19 outbreak. ![]() 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. We illustrate this through the novel coronavirus disease (COVID-19) as a substantive case study. 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. ![]() While these self-exciting processes have a simple formulation, they can model incredibly complex phenomena. Hawkes processes are a form of self-exciting process that has been used in numerous applications, including neuroscience, seismology, and terrorism. ![]()
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