COMPARISON OF HAWKES AND SEIR MODELS FOR THE SPREAD OF COVID-19

Two models that capture the spread of infectious diseases, the Hawkes point process model and the SEIR compartmental model, are compared with regard to their use in modeling the Covid-19 pandemic. The physical plausibility of the SEIR model is weighed against the parsimony and flexibility of the Hawkes model. The mathematical connection between Hawkes and SEIR models is described. ∗Department of Statistics, University of California Los Angeles †Department of Computer and Information Science, Indiana University Purdue University Indianapolis MSC 2020 subject classifications. Primary-60G55; secondary-92D30

[1]  Jesus R. Artalejo,et al.  The stochastic SEIR model before extinction: Computational approaches , 2015, Appl. Math. Comput..

[2]  F. Schoenberg,et al.  Residual analysis methods for space--time point processes with applications to earthquake forecast models in California , 2011, 1202.6487.

[3]  A. MOSAVI,et al.  COVID-19 Outbreak Prediction with Machine Learning , 2020, medRxiv.

[4]  F. Schoenberg,et al.  Nonparametric estimation of variable productivity Hawkes processes , 2020, Environmetrics.

[5]  A. Hawkes,et al.  A cluster process representation of a self-exciting process , 1974, Journal of Applied Probability.

[6]  HighWire Press.  Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character , 1934 .

[7]  Frederic Paik Schoenberg,et al.  Evaluation of space–time point process models using super‐thinning , 2011 .

[8]  Yves Lecourtier,et al.  Unidentifiable compartmental models: what to do? , 1981 .

[9]  Elisa Franco,et al.  The challenges of modeling and forecasting the spread of COVID-19 , 2020, Proceedings of the National Academy of Sciences.

[10]  Ulrike Goldschmidt,et al.  An Introduction To The Theory Of Point Processes , 2016 .

[11]  Junhyung Park,et al.  A non-parametric Hawkes model of the spread of Ebola in west Africa , 2020, Journal of applied statistics.

[12]  Daniel Eichner,et al.  Seroprevalence of SARS-CoV-2-Specific Antibodies Among Adults in Los Angeles County, California, on April 10-11, 2020. , 2020, JAMA.

[13]  J. Wallinga,et al.  Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures , 2004, American journal of epidemiology.

[14]  J. D. Zechar,et al.  The Collaboratory for the Study of Earthquake Predictability: Achievements and Priorities , 2018, Seismological Research Letters.

[15]  Jamol Pender,et al.  The Queue-Hawkes Process: Ephemeral Self-Excitement , 2018, 1811.04282.

[16]  Ah Sung Yang.  Modeling the Transmission Dynamics of Pertussis Using Recursive Point Process and SEIR model , 2019 .

[17]  R. Gloaguen,et al.  COVID-19 Pandemic Prediction for Hungary; a Hybrid Machine Learning Approach , 2020, medRxiv.

[18]  Xiaolong Qi,et al.  Real estimates of mortality following COVID-19 infection , 2020, The Lancet Infectious Diseases.

[19]  Danijel Schorlemmer,et al.  Voronoi residuals and other residual analyses applied to CSEP earthquake forecasts , 2015 .

[20]  Igor Linkov,et al.  US Army Engineer Research and Development Center , 2014 .

[21]  George Mohler,et al.  Modeling and estimation of multi-source clustering in crime and security data , 2013, 1311.7279.

[22]  J. Ioannidis,et al.  COVID-19 antibody seroprevalence in Santa Clara County, California , 2020, medRxiv.

[23]  A L Lloyd,et al.  Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[24]  Andrew J. Whalen,et al.  Identifiability of infection model parameters early in an epidemic , 2020, medRxiv.

[25]  Marc Hoffmann,et al.  A recursive point process model for infectious diseases , 2017, Annals of the Institute of Statistical Mathematics.

[26]  R. Cowan.  An introduction to the theory of point processes , 1978 .

[27]  Dave Higdon,et al.  Forecasting seasonal influenza with a state-space SIR model. , 2017, The annals of applied statistics.

[28]  Hannah R. Meredith,et al.  A scenario modeling pipeline for COVID-19 emergency planning , 2020, Scientific Reports.

[29]  Swapnil Mishra,et al.  SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations , 2017, WWW.

[30]  Yuan Zhang,et al.  Estimation of the time-varying reproduction number of COVID-19 outbreak in China , 2020, International Journal of Hygiene and Environmental Health.

[31]  M. J. Chapman,et al.  The structural identifiability of the susceptible infected recovered model with seasonal forcing. , 2005, Mathematical biosciences.

[32]  X. Liu,et al.  Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates , 2020, International Journal of Forecasting.

[33]  Alex Reinhart,et al.  A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications , 2017, Statistical Science.

[34]  F. Schoenberg,et al.  Nonparametric estimation of recursive point processes with application to mumps in Pennsylvania , 2021, Biometrical journal. Biometrische Zeitschrift.

[35]  Alessandro Vespignani,et al.  Containing the accidental laboratory escape of potential pandemic influenza viruses , 2013, BMC Medicine.

[36]  K. R. Godfrey,et al.  Identifiability and indistinguishability of linear compartmental models , 1990 .

[37]  D. Vere-Jones,et al.  Analyzing earthquake clustering features by using stochastic reconstruction , 2004 .

[38]  M. Day.  Covid-19: identifying and isolating asymptomatic people helped eliminate virus in Italian village , 2020, BMJ.

[39]  Imperial College COVID-19 Response Team,et al.  Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in European countries: technical description update , 2020, 2004.11342.

[40]  P. Montagnon.  A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale , 2018, Journal of mathematical biology.

[41]  C P Farrington,et al.  Branching process models for surveillance of infectious diseases controlled by mass vaccination. , 2003, Biostatistics.

[42]  Leonhard Held,et al.  Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance , 2014, ArXiv.

[43]  L. Allen.  Some discrete-time SI, SIR, and SIS epidemic models. , 1994, Mathematical biosciences.

[44]  D. Marsan,et al.  Extending Earthquakes' Reach Through Cascading , 2008, Science.

[45]  F. Schoenberg,et al.  Investigating Clustering and Violence Interruption in Gang-Related Violent Crime Data Using Spatial–Temporal Point Processes With Covariates , 2021, Journal of the American Statistical Association.

[46]  G. Shedler,et al.  Simulation of Nonhomogeneous Poisson Processes by Thinning , 1979 .

[47]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[48]  P. O’Neill,et al.  Bayesian estimation of the basic reproduction number in stochastic epidemic models , 2008 .

[49]  C. Whittaker,et al.  Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand , 2020 .

[50]  J. Rasmussen.  Bayesian Inference for Hawkes Processes , 2013 .

[51]  Frederic Paik Schoenberg,et al.  A NOTE ON THE CONSISTENT ESTIMATION OF SPATIAL-TEMPORAL POINT PROCESS PARAMETERS , 2015 .

[52]  G. Chowell,et al.  Transmission dynamics and control of Ebola virus disease (EVD): a review , 2014, BMC Medicine.

[53]  Junhyung Park,et al.  Real-time predictions of the 2018–2019 Ebola virus disease outbreak in the Democratic Republic of the Congo using Hawkes point process models , 2019, Epidemics.

[54]  Yosihiko Ogata,et al.  On Lewis' simulation method for point processes , 1981, IEEE Trans. Inf. Theory.

[55]  Y. Ogata.  The asymptotic behaviour of maximum likelihood estimators for stationary point processes , 1978 .

[56]  B. Finkenstädt,et al.  Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study , 2006, Biometrics.

[57]  Grant D. Brown,et al.  Bayesian compartmental model for an infectious disease with dynamic states of infection , 2018, Journal of applied statistics.

[58]  Y. Ogata.  Space-Time Point-Process Models for Earthquake Occurrences , 1998 .

[59]  Nicholas P Jewell,et al.  Predictive Mathematical Models of the COVID-19 Pandemic: Underlying Principles and Value of Projections. , 2020, JAMA.

[60]  S. Chen,et al.  Better Strategies for Containing COVID-19 Epidemics --- A Study of 25 Countries via an Extended Varying Coefficient SEIR Model , 2020, medRxiv.

[61]  N. Grassly,et al.  Mathematical models of infectious disease transmission , 2008, Nature Reviews Microbiology.

[62]  J. D. Zechar,et al.  Regional Earthquake Likelihood Models I: First-Order Results , 2013 .

[63]  Frederic Paik Schoenberg,et al.  Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts , 2014, 1501.06387.

[64]  Pejman Rohani,et al.  Appropriate Models for the Management of Infectious Diseases , 2005, PLoS medicine.

[65]  Giovanni Luca Torrisi,et al.  Risk Processes with Non-stationary Hawkes Claims Arrivals , 2010 .

[66]  Christl A. Donnelly,et al.  Real-time Estimates in Early Detection of SARS , 2006, Emerging infectious diseases.

[67]  C. Hernandez-Suarez,et al.  [Mathematical models for infectious diseases]. , 2007, Salud publica de Mexico.

[68]  C. Dye,et al.  Modeling the SARS Epidemic , 2003, Science.

[69]  Sen Pei,et al.  Projection of COVID-19 Cases and Deaths in the US as Individual States Re-open May 4,2020 , 2020, medRxiv.

[70]  J. J. G'omez-Cadenas,et al.  A simple formulation of non-Markovian SEIR , 2020, 2005.09975.

[71]  Philippe Lambert,et al.  Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone. , 2016, Biostatistics.

[72]  Yosihiko Ogata,et al.  Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes , 1988 .

[73]  Xihong Lin,et al.  Association of Public Health Interventions With the Epidemiology of the COVID-19 Outbreak in Wuhan, China. , 2020, JAMA.

[74]  Nicolas Hengartner,et al.  Quantifying Model Form Uncertainty of Epidemic Forecasting Models from Incidence Data , 2018, Online Journal of Public Health Informatics.

[75]  P. O’Neill.  Introduction and snapshot review: Relating infectious disease transmission models to data , 2010, Statistics in medicine.

[76]  Travis C. Porco,et al.  Real-time projections of epidemic transmission and estimation of vaccination impact during an Ebola virus disease outbreak in the Eastern region of the Democratic Republic of Congo , 2018, bioRxiv.

[77]  Gerardo Chowell,et al.  Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models , 2019, Theoretical Biology and Medical Modelling.