The challenges of modeling and forecasting the spread of COVID-19

Significance The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remain a challenge. Here, we present and detail three regional-scale models for forecasting and assessing the course of the pandemic. This work is intended to demonstrate the utility of parsimonious models for understanding the pandemic and to provide an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies. The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remains a challenge. Here, we detail three regional-scale models for forecasting and assessing the course of the pandemic. This work demonstrates the utility of parsimonious models for early-time data and provides an accessible framework for generating policy-relevant insights into its course. We show how these models can be connected to each other and to time series data for a particular region. Capable of measuring and forecasting the impacts of social distancing, these models highlight the dangers of relaxing nonpharmaceutical public health interventions in the absence of a vaccine or antiviral therapies.

[1]  Christl A. Donnelly,et al.  Estimates of the severity of coronavirus disease 2019: a model-based analysis , 2020, The Lancet Infectious Diseases.

[2]  Yang Liu,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[3]  ThaiBinh Luong,et al.  Modeling Epidemics With Compartmental Models. , 2020, JAMA.

[4]  J. Rocklöv,et al.  The reproductive number of COVID-19 is higher compared to SARS coronavirus , 2020, Journal of travel medicine.

[5]  A. Stomakhin,et al.  Reconstruction of missing data in social networks based on temporal patterns of interactions , 2011 .

[6]  S. Yadlowsky,et al.  Estimation of SARS-CoV-2 Infection Prevalence in Santa Clara County , 2020, medRxiv.

[7]  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.

[8]  M. Mello,et al.  Thinking Globally, Acting Locally - The U.S. Response to Covid-19. , 2020, The New England journal of medicine.

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

[10]  Eric H. Y. Lau,et al.  The Effective Reproduction Number of Pandemic Influenza: Prospective Estimation , 2010, Epidemiology.

[11]  C. Althaus,et al.  Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020 , 2020, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

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

[13]  Anita Lerch,et al.  Estimating unobserved SARS-CoV-2 infections in the United States , 2020, Proceedings of the National Academy of Sciences.

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

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

[16]  C. Zheng,et al.  Time Course of Lung Changes On Chest CT During Recovery From 2019 Novel Coronavirus (COVID-19) Pneumonia , 2020, Radiology.

[17]  M. K. Mak,et al.  Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates , 2014, Appl. Math. Comput..

[18]  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.

[19]  Maroussia Slavtchova-Bojkova,et al.  Bayesian estimation of the offspring mean in branching processes: Application to infectious disease data , 2012, Comput. Math. Appl..

[20]  Tianyi Li Simulating the spread of epidemics in China on multi-layer transportation networks: Beyond COVID-19 in Wuhan , 2020, EPL (Europhysics Letters).

[21]  Yu Wang,et al.  Curating a COVID-19 data repository and forecasting county-level death counts in the United States , 2020, Harvard Data Science Review.

[22]  Pierre-Yves Boëlle,et al.  The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks , 2012, BMC Medical Informatics and Decision Making.

[23]  Joel C. Miller,et al.  A Note on the Derivation of Epidemic Final Sizes , 2012, Bulletin of mathematical biology.

[24]  Andrea L. Bertozzi,et al.  Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes , 2016 .

[25]  Martin B. Short,et al.  Analyzing the World-Wide Impact of Public Health Interventions on the Transmission Dynamics of COVID-19 , 2020, 2004.01714.

[26]  Joel C. Miller,et al.  Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes , 2016, bioRxiv.

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

[28]  Christian L. Althaus,et al.  Pattern of early human-to-human transmission of Wuhan 2019-nCoV , 2020, bioRxiv.

[29]  Pavel Dedera,et al.  Mathematical Modelling of Study , 2011 .

[30]  Carlos Castillo-Chavez,et al.  Mathematical Models in Epidemiology , 2019, Texts in Applied Mathematics.

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

[32]  S. Eubank,et al.  Commentary on Ferguson, et al., “Impact of Non-pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand” , 2020, Bulletin of Mathematical Biology.

[33]  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.

[34]  Andrea L. Bertozzi,et al.  Point-process models of social network interactions: Parameter estimation and missing data recovery , 2015, European Journal of Applied Mathematics.

[35]  P. Klepac,et al.  Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts , 2020, The Lancet Global Health.

[36]  L Forsberg White,et al.  A likelihood‐based method for real‐time estimation of the serial interval and reproductive number of an epidemic , 2008, Statistics in medicine.

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

[38]  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.

[39]  Carl Kitchens,et al.  Health Divided: Public Health and Individual Medicine in the Making of the Modern American State by Daniel Sledge (review) , 2018 .

[40]  C. Zheng,et al.  Time Course of Lung Changes at Chest CT during Recovery from Coronavirus Disease 2019 (COVID-19) , 2020 .

[41]  G. DeFriese,et al.  The New York Times , 2020, Publishing for Libraries.

[42]  Dennis Andersson,et al.  A retrospective cohort study , 2018 .

[43]  Ping Yan,et al.  Distribution Theory, Stochastic Processes and Infectious Disease Modelling , 2008, Mathematical Epidemiology.

[44]  E. Dong,et al.  An interactive web-based dashboard to track COVID-19 in real time , 2020, The Lancet Infectious Diseases.

[45]  Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China , 2020, Nature Medicine.

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

[47]  Fred Brauer,et al.  Compartmental Models in Epidemiology , 2008, Mathematical Epidemiology.

[48]  Neil M. Ferguson,et al.  The effect of public health measures on the 1918 influenza pandemic in U.S. cities , 2007, Proceedings of the National Academy of Sciences.

[49]  J. Gómez-Gardeñes,et al.  A mathematical model for the spatiotemporal epidemic spreading of COVID19 , 2020, medRxiv.

[50]  P. Klepac,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

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

[52]  H. Akaike A new look at the statistical model identification , 1974 .

[53]  L. Gostin,et al.  The Novel Coronavirus Originating in Wuhan, China: Challenges for Global Health Governance. , 2020, JAMA.

[54]  C. Murray Forecasting COVID-19 impact on hospital bed-days, ICU-days, ventilator-days and deaths by US state in the next 4 months , 2020, medRxiv.

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

[56]  Jing Zhao,et al.  Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia , 2020, The New England journal of medicine.

[57]  G. Leung,et al.  Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study , 2020, The Lancet.

[58]  Wing Yin Venus Lau,et al.  Transmission interval estimates suggest pre-symptomatic spread of COVID-19 , 2020, medRxiv.

[59]  J. Xiang,et al.  Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study , 2020, The Lancet.

[60]  Qun Li Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia , 2020 .

[61]  C. Fraser,et al.  Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions , 2003, Science.