Identification of Time Delays in COVID-19 Data

COVID-19 data released by public health authorities features the presence of notable time-delays, corresponding to the difference between actual time of infection and identification of infection. These delays have several causes, including the natural incubation period of the virus, availability and speed of testing facilities, population demographics, and testing center capacity, among others. Such delays have important ramifications for both the mathematical modeling of COVID-19 contagion and the design and evaluation of intervention strategies. In the present work, we introduce a novel optimization technique for the identification of time delays in COVID-19 data, making use of a delay-differential equation model. The proposed method is general in nature and may be applied not only to COVID-19, but for generic dynamical systems in which time delays may be present.

[1]  S. Dhamodharavadhani,et al.  SEIR Model for COVID-19 Epidemic Using Delay Differential Equation , 2021 .

[2]  Krishna Garikipati,et al.  System inference for the spatio-temporal evolution of infectious diseases: Michigan in the time of COVID-19 , 2020, Computational Mechanics.

[3]  A. Rinaldo,et al.  Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures , 2020, Proceedings of the National Academy of Sciences.

[4]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[5]  Giuseppe C. Calafiore,et al.  A Modified SIR Model for the COVID-19 Contagion in Italy , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[6]  Alvaro L. G. A. Coutinho,et al.  Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models , 2020, Computational Mechanics.

[7]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[8]  O Diekmann,et al.  On the formulation of epidemic models (an appraisal of Kermack and McKendrick) , 2012, Journal of biological dynamics.

[9]  T. I. Zohdi,et al.  An agent-based computational framework for simulation of global pandemic and social response on planet X , 2020, Computational Mechanics.

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

[11]  Thomas E. Yankeelov,et al.  Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study , 2020, Computational mechanics.

[12]  F. Bertrand,et al.  Least-Squares Finite Element Method for a Meso-Scale Model of the Spread of COVID-19 , 2021, Comput..

[13]  M. R. Ferrández,et al.  Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China , 2020, Communications in Nonlinear Science and Numerical Simulation.

[14]  Giacomo Dimarco,et al.  Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics , 2021, 2110.00293.

[15]  Lorenzo Pareschi,et al.  Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of Covid-19 in Italy , 2021, Mathematical Models and Methods in Applied Sciences.

[16]  Thomas E. Yankeelov,et al.  Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion , 2020, Applied Mathematics Letters.

[17]  Oliver Stoner,et al.  A modelling approach for correcting reporting delays in disease surveillance data , 2017, Statistics in medicine.

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

[19]  Nicola Guglielmi,et al.  Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID‐19 , 2021, Mathematical methods in the applied sciences.

[20]  Gabriel F. Barros,et al.  Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil , 2021, Archives of Computational Methods in Engineering.

[21]  G. Remuzzi,et al.  COVID-19 and Italy: what next? , 2020, The Lancet.

[22]  Alessandro Reali,et al.  Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems , 2021, Computer Methods in Applied Mechanics and Engineering.

[23]  Alessandro Reali,et al.  Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations , 2021, Engineering with Computers.

[24]  P. F. Antonietti,et al.  SUIHTER: a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy , 2021, Proceedings of the Royal Society A.

[25]  Yasuhiro Takeuchi,et al.  Global asymptotic properties of a delay SIR epidemic model with finite incubation times , 2000 .

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

[27]  M. Iannelli,et al.  An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka , 2014 .

[28]  Sunhwa Choi,et al.  Estimating the reproductive number and the outbreak size of COVID-19 in Korea , 2020, Epidemiology and Health.

[29]  J. Forde,et al.  Delay differential equation models in mathematical biology. , 2005 .

[30]  Deborah Lacitignola,et al.  Global stability of an SIR epidemic model with information dependent vaccination. , 2008, Mathematical biosciences.

[31]  A. J. Sarnaglia,et al.  Correcting notification delay and forecasting of COVID-19 data , 2021, Journal of Mathematical Analysis and Applications.

[32]  Mohamed Aziz Bhouri,et al.  COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior , 2020, Computer Methods in Applied Mechanics and Engineering.

[33]  Fabiana Zama,et al.  Monitoring Italian COVID-19 spread by a forced SEIRD model , 2020, PloS one.

[34]  L. Dell’Anna.  Solvable delay model for epidemic spreading: the case of Covid-19 in Italy , 2020, Scientific Reports.

[35]  Hannah R. Meredith,et al.  The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application , 2020, Annals of Internal Medicine.

[36]  J Tinsley Oden,et al.  Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models , 2020, Computational mechanics.

[37]  Pushpendra Kumar,et al.  The analysis of a time delay fractional COVID‐19 model via Caputo type fractional derivative , 2020, Mathematical methods in the applied sciences.

[38]  K. Linka,et al.  Is it safe to lift COVID-19 travel bans? The Newfoundland story. , 2020, Computational Mechanics.