September  2021, 3(3): 479-541. doi: 10.3934/fods.2021022

A study of disproportionately affected populations by race/ethnicity during the SARS-CoV-2 pandemic using multi-population SEIR modeling and ensemble data assimilation

1. 

Florida Atlantic University, 777 Glades Rd., Boca Raton, FL 33431, USA

2. 

University of North Carolina, 130 Mason Farm Road Chapel Hill, NC 27599, USA

3. 

University of Michigan, 530 Church St, Ann Arbor, MI 48109, USA

4. 

Arizona State University, 1151 S Forest Ave, Tempe, AZ 85281, USA

5. 

Smith College, Northampton, MA 01063, USA

6. 

NORCE Norwegian Research Centre AS, Nygårdsporten 112, 5008 Bergen, Norway

Received  January 2021 Revised  August 2021 Published  September 2021 Early access  September 2021

Fund Project: The second author (CSS) is supported by the US Office of Naval Research under grant N00014-18-1-2204. The third author (DPM) is supported by the NSF GRFP DGE 1256260. The seventh author (GE) was supported by internal funding from NORCE

The disparity in the impact of COVID-19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number ($ R_t $), can be hard to calculate from this data especially for individual populations. Furthermore, disparities in the availability of testing, record keeping infrastructure, or government funding in disadvantaged populations can produce incomplete data sets. In this work, we apply ensemble data assimilation techniques which optimally combine model and data to produce a more complete data set providing better estimates of the critical metrics used by public health officials and epidemiologists. We employ a multi-population SEIR (Susceptible, Exposed, Infected and Recovered) model with a time dependent reproductive number and age stratified contact rate matrix for each population. We assimilate the daily death data for populations separated by ethnic/racial groupings using a technique called Ensemble Smoothing with Multiple Data Assimilation (ESMDA) to estimate model parameters and produce an $R_t(n)$ for the $n^{th}$ population. We do this with three distinct approaches, (1) using the same contact matrices and prior $R_t(n)$ for each population, (2) assigning contact matrices with increased contact rates for working age and older adults to populations experiencing disparity and (3) as in (2) but with a time-continuous update to $R_t(n)$. We make a study of 9 U.S. states and the District of Columbia providing a complete time series of the pandemic in each and, in some cases, identifying disparities not otherwise evident in the aggregate statistics.

Citation: Emmanuel Fleurantin, Christian Sampson, Daniel Paul Maes, Justin Bennett, Tayler Fernandes-Nunez, Sophia Marx, Geir Evensen. A study of disproportionately affected populations by race/ethnicity during the SARS-CoV-2 pandemic using multi-population SEIR modeling and ensemble data assimilation. Foundations of Data Science, 2021, 3 (3) : 479-541. doi: 10.3934/fods.2021022
References:
[1]

Cyberstates 2020: The definitive guide to the U.S. tech industry and tech wrokforce, URL https://www.cyberstates.org, Last accessed 2021-04-13. Google Scholar

[2]

Disparities in Wealth by Race and Ethnicity in the 2019 Survey of Consumer Finances, URL https://www.federalreserve.gov/econres/notes/feds-notes/disparities-in-wealth-by-race-and-ethnicity-in-the-2019-survey-of-consumer-finances-20200928.htm, Last accessed 2021-04-13. Google Scholar

[3]

Diversity in high tech, URL https://www.eeoc.gov/special-report/diversity-high-tech, Last accessed 2021-04-13. Google Scholar

[4]

Economy at a Glance: California, URL https://data.bls.gov/timeseries/LASST060000000000006?, Last accessed 2021-04-13. Google Scholar

[5]

IHME COVID-19 estimates, URL http://www.healthdata.org/covid/data-downloads, Last accessed 2021-04-13. Google Scholar

[6]

Options to Reduce Quarantine for Contacts of Persons with SARS-CoV-2 Infection Using Symptom Monitoring and Diagnostic Testing, URL https://www.cdc.gov/coronavirus/2019-ncov/more/scientific-brief-options-to-reduce-quarantine.html, Last accessed 2021-04-13. Google Scholar

[7]

Racial Data Dashboard, 2021, URL https://covidtracking.com/race/dashboard, Last accessed 2021-04-13. Google Scholar

[8]

Risk for covid-19 infection, hospitalization, and death by race/ethnicity, URL https://www.cdc.gov/coronavirus/2019-ncov/covid-data/investigations-discovery/hospitalization-death-by-race-ethnicity.html, Last accessed 2021-08-03. Google Scholar

[9]

Rt COVID-19, URL https://rt.live/, Last accessed 2021-04-13. Google Scholar

[10]

Statistics and Church Facts | Total Church Membership, URL http://newsroom.churchofjesuschrist.org/facts-and-statistics/state/utah, Last accessed 2021-07-31. Google Scholar

[11]

E. Armstrong, M. Runge and J. Gerardin, Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation, Infectious Disease Modelling. Google Scholar

[12]

M. Asch, M. Bocquet and M. Nodet, Data Assimilation: Methods, Algorithms, and Applications, SIAM, Society for Industrial and Applied Mathematics, 2016. doi: 10.1137/1.9781611974546.pt1.  Google Scholar

[13]

L. M. A. Bettencourt, R. M. Ribeiro, G. Chowell, T. Lant and C. Castillo-Chavez, Towards real time epidemiology: Data assimilation, modeling and anomaly detection of health surveillance data streams, Lecture Notes in Computer Science Intelligence and Security Informatics: Biosurveillance, 79–90. doi: 10.1007/978-3-540-72608-1_8.  Google Scholar

[14]

M. Bocquet and P. Sakov, An iterative ensemble Kalman smoother, Quarterly Journal of the Royal Meteorological Society, 140 (2013), 1521-1535.  doi: 10.1002/qj.2236.  Google Scholar

[15]

A. Carrassi, M. Bocquet, L. Bertino and G. Evensen, Data assimilation in the geosciences: An overview on methods issues and perspectives, WCC, 9 2018. doi: 10.1002/wcc.535.  Google Scholar

[16]

A. A. Emerick and A. C. Reynolds, Ensemble smoother with multiple data assimilation, Computers & Geosciences, 55 (2013), 3-15.  doi: 10.1016/j.cageo.2012.03.011.  Google Scholar

[17]

G. Evensen, Analysis of iterative ensemble smoothers for solving inverse problems, Computational Geosciences, 22 (2018), 885-908.  doi: 10.1007/s10596-018-9731-y.  Google Scholar

[18]

G. Evensen, J. Amezcua, M. Bocquet, A. Carrassi, A. Farchi, A. Fowler, P. L. Houtekamer, C. K. Jones, R. J. de Moraes, M. Pulido, C. Sampson and F. C. Vossepoel, An international initiative of predicting the SARS-CoV-2 pandemic using ensemble data assimilation, Foundations of Data Science, (2020). doi: 10.3934/fods.2021001.  Google Scholar

[19]

J. R. EyreS. J. English and M. Forsythe, Assimilation of satellite data in numerical weather prediction. part i: The early years, Quarterly Journal of the Royal Meteorological Society, 146 (2019), 49-68.  doi: 10.1002/qj.3654.  Google Scholar

[20]

A. L. Garcia-Basteiro, G. Moncunill, M. Tortajada, M. Vidal, C. Guinovart, A. Jiménez, R. Santano, S. Sanz, S. Méndez, A. Llupià, R. Aguilar, S. Alonso, D. Barrios, C. Carolis, P. Cisteró, E. Chóliz, A. Cruz, S. Fochs, C. Jairoce, J. Hecht, M. Lamoglia, M. J. Martínez, R. A. Mitchell, N. Ortega, N. Pey, L. Puyol, M. Ribes, N. Rosell, P. Sotomayor, S. Torres, S. Williams, S. Barroso, A. Vilella, J. Muñoz, A. Trilla, P. Varela, A. Mayor and C. Dobaño, Seroprevalence of antibodies against SARS-CoV-2 among health care workers in a large spanish reference hospital, Nature Communications, 11 (2020), Article number: 3500. doi: 10.1038/s41467-020-17318-x.  Google Scholar

[21]

C. G. Grijalva, M. A. Rolfes, Y. Zhu, H. Q. McLean, K. E. Hanson, E. A. Belongia, N. B. Halasa, A. Kim, C. Reed, A. M. Fry and H. K. Talbot, Transmission of SARS-COV-2 infections in households - Tennessee and Wisconsin, April-September 2020, MMWR. Morbidity and Mortality Weekly Report, 69 (2020), 1631–1634. doi: 10.15585/mmwr.mm6944e1.  Google Scholar

[22]

P. L. Houtekamer and F. Zhang, Review of the ensemble kalman filter for atmospheric data assimilation, Monthly Weather Review, 144 (2016), 4489-4532.  doi: 10.1175/MWR-D-15-0440.1.  Google Scholar

[23]

J. P. A. Ioannidis, Infection fatality rate of COVID-19 inferred from seroprevalence data, Bulletin of the World Health Organization, 99 (2020), 19–33F. doi: 10.2471/blt.20.265892.  Google Scholar

[24]

J. Jeppesen, Fact sheet: Reanalysis, URL https://www.ecmwf.int/en/about/media-centre/focus/2020/fact-sheet-reanalysis, 2020, Last accessed 2021-07-31. Google Scholar

[25]

E. J. KostelichY. KuangJ. M. McdanielN. Z. MooreN. L. Martirosyan and M. C. Preul, Accurate state estimation from uncertain data and models: An application of data assimilation to mathematical models of human brain tumors, Biology Direct, 6 (2011), 64.  doi: 10.1186/1745-6150-6-64.  Google Scholar

[26]

W. Lieberman-CribbinS. TuminelloR. M. Flores and E. Taioli, Disparities in COVID-19 testing and positivity in new york city, American Journal of Preventive Medicine, 59 (2020), 326-332.  doi: 10.1016/j.amepre.2020.06.005.  Google Scholar

[27]

N. Narea, Immigrants have helped keep essential services running. But those without legal status have no financial safety net, URL https://www.vox.com/2020/5/5/21244630/undocumented-immigrants-coronavirus-relief-cares-act, 2020, Last accessed 2021-07-31. Google Scholar

[28]

I. Pathak, Y. Choi, D. Jiao, D. Yeung and L. Liu, Racial-ethnic disparities in case fatality ratio narrowed after age standardization: A call for race-ethnicity-specific age distributions in state covid-19 data, MedRxiv, (2020). doi: 10.1101/2020.10.01.20205377.  Google Scholar

[29]

J. Skjervheim, G. Evensen, J. Hove and J. G. Vabø, An ensemble smoother for assisted history matching, SPE, (2011), 141929. doi: 10.2118/141929-MS.  Google Scholar

[30]

A. S. Stordal and A. H. Elsheikh, Iterative ensemble smoothers in the annealed importance sampling framework, Advances in Water Resources, 86 (2015), 231-239.  doi: 10.1016/j.advwatres.2015.09.030.  Google Scholar

[31]

G. VernieresA. AnisR. N. Miller and L. L. Ehret, Generalized inversion of thermistor-chain data and a layer model of lake kinneret, Ocean Modelling, 12 (2006), 112-139.  doi: 10.1016/j.ocemod.2005.04.004.  Google Scholar

[32]

Z. WuT. PhanJ. BaezY. Kuang and E. J. Kostelich, Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy, Mathematical Biosciences and Engineering, 16 (2019), 3512-3536.  doi: 10.3934/mbe.2019176.  Google Scholar

show all references

References:
[1]

Cyberstates 2020: The definitive guide to the U.S. tech industry and tech wrokforce, URL https://www.cyberstates.org, Last accessed 2021-04-13. Google Scholar

[2]

Disparities in Wealth by Race and Ethnicity in the 2019 Survey of Consumer Finances, URL https://www.federalreserve.gov/econres/notes/feds-notes/disparities-in-wealth-by-race-and-ethnicity-in-the-2019-survey-of-consumer-finances-20200928.htm, Last accessed 2021-04-13. Google Scholar

[3]

Diversity in high tech, URL https://www.eeoc.gov/special-report/diversity-high-tech, Last accessed 2021-04-13. Google Scholar

[4]

Economy at a Glance: California, URL https://data.bls.gov/timeseries/LASST060000000000006?, Last accessed 2021-04-13. Google Scholar

[5]

IHME COVID-19 estimates, URL http://www.healthdata.org/covid/data-downloads, Last accessed 2021-04-13. Google Scholar

[6]

Options to Reduce Quarantine for Contacts of Persons with SARS-CoV-2 Infection Using Symptom Monitoring and Diagnostic Testing, URL https://www.cdc.gov/coronavirus/2019-ncov/more/scientific-brief-options-to-reduce-quarantine.html, Last accessed 2021-04-13. Google Scholar

[7]

Racial Data Dashboard, 2021, URL https://covidtracking.com/race/dashboard, Last accessed 2021-04-13. Google Scholar

[8]

Risk for covid-19 infection, hospitalization, and death by race/ethnicity, URL https://www.cdc.gov/coronavirus/2019-ncov/covid-data/investigations-discovery/hospitalization-death-by-race-ethnicity.html, Last accessed 2021-08-03. Google Scholar

[9]

Rt COVID-19, URL https://rt.live/, Last accessed 2021-04-13. Google Scholar

[10]

Statistics and Church Facts | Total Church Membership, URL http://newsroom.churchofjesuschrist.org/facts-and-statistics/state/utah, Last accessed 2021-07-31. Google Scholar

[11]

E. Armstrong, M. Runge and J. Gerardin, Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation, Infectious Disease Modelling. Google Scholar

[12]

M. Asch, M. Bocquet and M. Nodet, Data Assimilation: Methods, Algorithms, and Applications, SIAM, Society for Industrial and Applied Mathematics, 2016. doi: 10.1137/1.9781611974546.pt1.  Google Scholar

[13]

L. M. A. Bettencourt, R. M. Ribeiro, G. Chowell, T. Lant and C. Castillo-Chavez, Towards real time epidemiology: Data assimilation, modeling and anomaly detection of health surveillance data streams, Lecture Notes in Computer Science Intelligence and Security Informatics: Biosurveillance, 79–90. doi: 10.1007/978-3-540-72608-1_8.  Google Scholar

[14]

M. Bocquet and P. Sakov, An iterative ensemble Kalman smoother, Quarterly Journal of the Royal Meteorological Society, 140 (2013), 1521-1535.  doi: 10.1002/qj.2236.  Google Scholar

[15]

A. Carrassi, M. Bocquet, L. Bertino and G. Evensen, Data assimilation in the geosciences: An overview on methods issues and perspectives, WCC, 9 2018. doi: 10.1002/wcc.535.  Google Scholar

[16]

A. A. Emerick and A. C. Reynolds, Ensemble smoother with multiple data assimilation, Computers & Geosciences, 55 (2013), 3-15.  doi: 10.1016/j.cageo.2012.03.011.  Google Scholar

[17]

G. Evensen, Analysis of iterative ensemble smoothers for solving inverse problems, Computational Geosciences, 22 (2018), 885-908.  doi: 10.1007/s10596-018-9731-y.  Google Scholar

[18]

G. Evensen, J. Amezcua, M. Bocquet, A. Carrassi, A. Farchi, A. Fowler, P. L. Houtekamer, C. K. Jones, R. J. de Moraes, M. Pulido, C. Sampson and F. C. Vossepoel, An international initiative of predicting the SARS-CoV-2 pandemic using ensemble data assimilation, Foundations of Data Science, (2020). doi: 10.3934/fods.2021001.  Google Scholar

[19]

J. R. EyreS. J. English and M. Forsythe, Assimilation of satellite data in numerical weather prediction. part i: The early years, Quarterly Journal of the Royal Meteorological Society, 146 (2019), 49-68.  doi: 10.1002/qj.3654.  Google Scholar

[20]

A. L. Garcia-Basteiro, G. Moncunill, M. Tortajada, M. Vidal, C. Guinovart, A. Jiménez, R. Santano, S. Sanz, S. Méndez, A. Llupià, R. Aguilar, S. Alonso, D. Barrios, C. Carolis, P. Cisteró, E. Chóliz, A. Cruz, S. Fochs, C. Jairoce, J. Hecht, M. Lamoglia, M. J. Martínez, R. A. Mitchell, N. Ortega, N. Pey, L. Puyol, M. Ribes, N. Rosell, P. Sotomayor, S. Torres, S. Williams, S. Barroso, A. Vilella, J. Muñoz, A. Trilla, P. Varela, A. Mayor and C. Dobaño, Seroprevalence of antibodies against SARS-CoV-2 among health care workers in a large spanish reference hospital, Nature Communications, 11 (2020), Article number: 3500. doi: 10.1038/s41467-020-17318-x.  Google Scholar

[21]

C. G. Grijalva, M. A. Rolfes, Y. Zhu, H. Q. McLean, K. E. Hanson, E. A. Belongia, N. B. Halasa, A. Kim, C. Reed, A. M. Fry and H. K. Talbot, Transmission of SARS-COV-2 infections in households - Tennessee and Wisconsin, April-September 2020, MMWR. Morbidity and Mortality Weekly Report, 69 (2020), 1631–1634. doi: 10.15585/mmwr.mm6944e1.  Google Scholar

[22]

P. L. Houtekamer and F. Zhang, Review of the ensemble kalman filter for atmospheric data assimilation, Monthly Weather Review, 144 (2016), 4489-4532.  doi: 10.1175/MWR-D-15-0440.1.  Google Scholar

[23]

J. P. A. Ioannidis, Infection fatality rate of COVID-19 inferred from seroprevalence data, Bulletin of the World Health Organization, 99 (2020), 19–33F. doi: 10.2471/blt.20.265892.  Google Scholar

[24]

J. Jeppesen, Fact sheet: Reanalysis, URL https://www.ecmwf.int/en/about/media-centre/focus/2020/fact-sheet-reanalysis, 2020, Last accessed 2021-07-31. Google Scholar

[25]

E. J. KostelichY. KuangJ. M. McdanielN. Z. MooreN. L. Martirosyan and M. C. Preul, Accurate state estimation from uncertain data and models: An application of data assimilation to mathematical models of human brain tumors, Biology Direct, 6 (2011), 64.  doi: 10.1186/1745-6150-6-64.  Google Scholar

[26]

W. Lieberman-CribbinS. TuminelloR. M. Flores and E. Taioli, Disparities in COVID-19 testing and positivity in new york city, American Journal of Preventive Medicine, 59 (2020), 326-332.  doi: 10.1016/j.amepre.2020.06.005.  Google Scholar

[27]

N. Narea, Immigrants have helped keep essential services running. But those without legal status have no financial safety net, URL https://www.vox.com/2020/5/5/21244630/undocumented-immigrants-coronavirus-relief-cares-act, 2020, Last accessed 2021-07-31. Google Scholar

[28]

I. Pathak, Y. Choi, D. Jiao, D. Yeung and L. Liu, Racial-ethnic disparities in case fatality ratio narrowed after age standardization: A call for race-ethnicity-specific age distributions in state covid-19 data, MedRxiv, (2020). doi: 10.1101/2020.10.01.20205377.  Google Scholar

[29]

J. Skjervheim, G. Evensen, J. Hove and J. G. Vabø, An ensemble smoother for assisted history matching, SPE, (2011), 141929. doi: 10.2118/141929-MS.  Google Scholar

[30]

A. S. Stordal and A. H. Elsheikh, Iterative ensemble smoothers in the annealed importance sampling framework, Advances in Water Resources, 86 (2015), 231-239.  doi: 10.1016/j.advwatres.2015.09.030.  Google Scholar

[31]

G. VernieresA. AnisR. N. Miller and L. L. Ehret, Generalized inversion of thermistor-chain data and a layer model of lake kinneret, Ocean Modelling, 12 (2006), 112-139.  doi: 10.1016/j.ocemod.2005.04.004.  Google Scholar

[32]

Z. WuT. PhanJ. BaezY. Kuang and E. J. Kostelich, Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy, Mathematical Biosciences and Engineering, 16 (2019), 3512-3536.  doi: 10.3934/mbe.2019176.  Google Scholar

Figure 1.  The general form of the $ R_{ij}^A(n) $ contact matrix elements for contact rates between age groups $ i $ and $ j $ in a given sub-population. The contact matrix is then subdivided into different blocks where parameters $ \alpha, \beta, \eta, \gamma, \varepsilon, \zeta, \delta_1, \delta_2, \delta_3, \xi_1, \xi_2, \xi_3 $ and $ \xi_4 $ control the contact rates between different age groups which generate similar patterns for spreading the disease. In particular, we define $ \gamma, \delta_2, \xi_2 $ and $ \xi_3 $ to be the parameters for the contact rates of the working class age groups
Figure 2.  $ \mathbf{R}^{\rm{A}} $ for the NDAP $ (i) $ and DAP $ (ii) $ in our runs without DA for each intervention period along with the $ \mathbf{R}^{\rm{C}} $ matrix $ (iii) $ used in these simulations. We also used the $ \mathbf{R}^{\rm{A}} $'s in $ (i) $ and $ (ii) $ for the DA runs
Figure 3.  Results for non-DA runs with DAP and NDAP at about the same population
Figure 4.  Results for non-DA runs with NDAP at $ 70\% $ of the total population
Figure 5.  Examples of analysis runs for various values of $ R^C_{nm} $ from the District of Columbia (DC). Top: left $ R^C_{nm} = 0 $, right $ R^C_{nm} = 10^{-3} $. Bottom: left $ R^C_{nm} = 10^{-1} $, right $ R^C_{nm} = 6\times10^{-1} $
Figure 6.  Analysis results for the District of Columbia (DC) with $ R^A_{ij}=1 $ and piece-wise updates to $ R_t(n) $
Figure 7.  Analysis results for the District of Columbia (DC) with age stratified $ R^A $ and piece-wise updates to $ R_t(n) $
Figure 8.  Analysis results for the continuous update case for the state of AK
Figure 9.  Analysis results for the continuous update case for the state of CA
Figure 10.  Analysis results for the continuous update case for the state of CT
Figure 11.  Analysis results for the continuous update case for the state of DE
Figure 12.  Analysis results for the continuous update case for the District of Columbia
Figure 13.  Analysis results for the continuous update case for the state of HI
Figure 14.  Analysis results for the continuous update case for the state of MD
Figure 15.  Analysis results for the continuous update case for the state of MI
Figure 16.  Analysis results for the continuous update case for the state of UT
Figure 17.  Analysis results for the continuous update case for the state of WA
Figure 18.  Analysis results when using piece-wise updates to $ R(t) $ for AK. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 19.  Analysis results when using piecewise updates to $ R(t) $ for CA. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 20.  Analysis results when using piecewise updates to $ R(t) $ for CT. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 21.  Analysis results when using piecewise updates to $ R(t) $ for DE. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 22.  Analysis results when using piecewise updates to $ R(t) $ for DC. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 23.  Analysis results when using piecewise updates to $ R(t) $ for HI. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 24.  Analysis results when using piecewise updates to $ R(t) $ for MD. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 25.  Analysis results when using piecewise updates to $ R(t) $ for MI. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 26.  Analysis results when using piecewise updates to $ R(t) $ for UT. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Figure 27.  Analysis results when using piecewise updates to $ R(t) $ for WA. Top row: $ R^A $ with entries of all ones. Bottom Row: $ R^A $ for DAPs and NDAPs
Table 5">Figure 28.  Analysis results with a CFR prior of $ 0.009 $ ($ \sigma_{CFR} = 0.05 $) and the same $ R_t(n) $ ($ \sigma_{R(t)} = 1.5 $) prior for all populations. This figure corresponds to columns 2 and 3 in Table 5
Table 5">Figure 29.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.05 $) and the same $ R_t(n) $ ($ \sigma_{R(t)} = 1.5 $) prior for all populations. This figure corresponds to columns 4 and 5 in Table 5
Table 5">Figure 30.  Analysis results with a CFR prior of $ 0.001 $ ($ \sigma_{CFR} = 0.03 $) and the same $ R_t(n) $ ($ \sigma_{R(t)} = 1.5 $) prior for all populations. This figure corresponds to columns 6 and 7 in Table 5
Table 6">Figure 31.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.05 $) and prior $ R_t(n) $ ($ \sigma_{R(t)} = 0.5 $) curves coming from initial piece-wise assimilation also assuming a $ 0.020 $ CFR prior. This figure corresponds to columns 2 and 3 in Table 6
Table 6">Figure 32.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.002 $) and prior $ R_t(n) $ ($ \sigma_{R(t)} = 0.5 $) curves coming from initial piece-wise assimilation also assuming a $ 0.020 $ CFR prior. This figure corresponds to columns 4 and 5 in Table 6
Table 7">Figure 33.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.05 $) for the Black population only and a CFR Prior of $ 0.009 $ ($ \sigma_{CFR} = 0.05 $) for all other populations. The prior $ R_t(n) $ ($ \sigma_{R(t)} = 1.5 $) curves are the same for all populations. This figure corresponds to columns 2 and 3 in Table 7
Table 7 and is the only case where Black infections can be lower than that of the LatinX population and still have more deaths">Figure 34.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.002 $) for the Black population only and a CFR Prior of $ 0.009 $ ($ \sigma_{CFR} = 0.0009 $) for all other populations. The prior $ R_t(n) $ ($ \sigma_{R(t)} = 0.5 $) curves coming from initial piece-wise assimilation also assuming a $ 0.020 $ CFR prior. This figure corresponds to columns 4 and 5 in Table 7 and is the only case where Black infections can be lower than that of the LatinX population and still have more deaths
Table 7">Figure 35.  Analysis results with a CFR prior of $ 0.020 $ ($ \sigma_{CFR} = 0.05 $) for the Black population only and a CFR Prior of $ 0.009 $ ($ \sigma_{CFR} = 0.05 $) for all other populations. The prior $ R_t(n) $ ($ \sigma_{R(t)} = 0.5 $) curves coming from initial piece-wise assimilation also assuming a $ 0.020 $ CFR prior. This figure corresponds to columns 6 and 7 in Table 7
Figure 36.  Analysis results for the continuous update case for the state of AK
Figure 37.  Analysis results for the continuous update case for the state of CA
Figure 38.  Analysis results for the continuous update case for the state of CT
Figure 39.  Analysis results for the continuous update case for the state of DC
Figure 40.  Analysis results for the continuous update case for the state of DE
Figure 41.  Analysis results for the continuous update case for the state of HI
Figure 42.  Analysis results for the continuous update case for the state of MD
Figure 43.  Analysis results for the continuous update case for the state of MI
Figure 44.  Analysis results for the continuous update case for the state of UT
Figure 45.  Analysis results for the continuous update case for the state of WA
Table 1.  Matrix scaling parameters for DAP and NDAP workers in lockdown and post-lockdown time periods
Scalings Matrix Parameters
$\alpha$ $\beta$ $\gamma$ $\eta$ $\epsilon$ $\zeta$ $\delta_1$ $\delta_2$ $\delta_3$ $\xi_1$ $\xi_2$ $\xi_3$ $\xi_4$
DAP lock 0.5 0.7 0.55 0.25 0.25 0.35 0.3 0.7 0.7 0.4 0.65 0.55 0.6
DAP post-lock 0.7 0.8 0.7 0.3 0.3 0.4 0.6 0.85 0.7 0.85 0.7 0.65 0.65
NDAP lock 0.5 0.7 0.5 0.2 0.2 0.3 0.3 0.6 0.7 0.4 0.6 0.5 0.6
NDAP post-lock 0.7 0.8 0.7 0.25 0.25 0.35 0.6 0.7 0.75 0.7 0.7 0.65 0.65
Scalings Matrix Parameters
$\alpha$ $\beta$ $\gamma$ $\eta$ $\epsilon$ $\zeta$ $\delta_1$ $\delta_2$ $\delta_3$ $\xi_1$ $\xi_2$ $\xi_3$ $\xi_4$
DAP lock 0.5 0.7 0.55 0.25 0.25 0.35 0.3 0.7 0.7 0.4 0.65 0.55 0.6
DAP post-lock 0.7 0.8 0.7 0.3 0.3 0.4 0.6 0.85 0.7 0.85 0.7 0.65 0.65
NDAP lock 0.5 0.7 0.5 0.2 0.2 0.3 0.3 0.6 0.7 0.4 0.6 0.5 0.6
NDAP post-lock 0.7 0.8 0.7 0.25 0.25 0.35 0.6 0.7 0.75 0.7 0.7 0.65 0.65
Table 2.  Date breakdown by intervention periods for all states and the District of Columbia
Interventions Information on Intervention Periods by State and the District of Columbia
AK CA CT DC DE HI MD MI UT WA
Start date 3/8/20 2/25/20 2/27/20 2/27/20 3/1/20 2/28/20 2/25/20 2/21/20 2/29/20 1/9/20
1st Phase 3/19/20 3/19/20 3/19/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20
2nd Phase 5/27/20 5/27/20 5/27/20 5/29/20 5/31/20 5/15/20 5/15/20 5/19/20 5/5/20 5/28/20
Interventions Information on Intervention Periods by State and the District of Columbia
AK CA CT DC DE HI MD MI UT WA
Start date 3/8/20 2/25/20 2/27/20 2/27/20 3/1/20 2/28/20 2/25/20 2/21/20 2/29/20 1/9/20
1st Phase 3/19/20 3/19/20 3/19/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20 3/17/20
2nd Phase 5/27/20 5/27/20 5/27/20 5/29/20 5/31/20 5/15/20 5/15/20 5/19/20 5/5/20 5/28/20
Table 3.  Demographic breakdown by race/ethnicity (where data is available) for all states and the District of Columbia. Groups that meet the criteria to be a DAP are in bold. AIAN = American Indian and Alaska Native, NHPI = Native Hawaiian and Pacific Islander
Race/Ethnicity Percentage of Population per State and the District of Columbia
AK CA CT DC DE HI MD MI UT WA
AIAN 0.15 0.076 X X X X X 0.005 0.023 0.01
Asian 0.06 0.14 0.04 0.0435 0.045 0.38 0.06 0.035 0.038 0.08
Black 0.03 0.06 0.1 0.4453 0.22 0.02 0.29 0.14 0.021 0.04
LatinX X 0.39 0.16 0.113 0.09 X 0.1 X 0.142 0.13
Multi X X 0.02 X 0.02 X X X X 0.05
NHPI 0.01 0.039 X X X 0.1 X X 0.016 0.008
Other 0.08 X 0.01 0.01 X 0.24 X 0.03 0.01 0.005
White 0.65 0.37 0.67 0.4196 0.62 0.25 0.51 0.78 0.78 0.69
Race/Ethnicity Percentage of Population per State and the District of Columbia
AK CA CT DC DE HI MD MI UT WA
AIAN 0.15 0.076 X X X X X 0.005 0.023 0.01
Asian 0.06 0.14 0.04 0.0435 0.045 0.38 0.06 0.035 0.038 0.08
Black 0.03 0.06 0.1 0.4453 0.22 0.02 0.29 0.14 0.021 0.04
LatinX X 0.39 0.16 0.113 0.09 X 0.1 X 0.142 0.13
Multi X X 0.02 X 0.02 X X X X 0.05
NHPI 0.01 0.039 X X X 0.1 X X 0.016 0.008
Other 0.08 X 0.01 0.01 X 0.24 X 0.03 0.01 0.005
White 0.65 0.37 0.67 0.4196 0.62 0.25 0.51 0.78 0.78 0.69
Table 5.  Results for the CFR using the same $ R_t(n) $ prior for all populations with $ \sigma_{R(t)} = 1.5 $
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=112 $ Prior, $ \sigma=0.05 $ Post, $ \chi^2=92 $ Prior, $ \sigma=0.03 $ Post, $ \chi^2=87 $
Asian 0.009 0.0074 0.020 0.0093 0.001 0.0070
Black 0.009 0.0126 0.020 0.0157 0.001 0.0084
LatinX 0.009 0.0213 0.020 0.0246 0.001 0.0147
Multi 0.009 0.0103 0.020 0.0104 0.001 0.0086
Other 0.009 0.0065 0.020 0.0042 0.001 0.0065
White 0.009 0.0229 0.020 0.0271 0.001 0.0134
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=112 $ Prior, $ \sigma=0.05 $ Post, $ \chi^2=92 $ Prior, $ \sigma=0.03 $ Post, $ \chi^2=87 $
Asian 0.009 0.0074 0.020 0.0093 0.001 0.0070
Black 0.009 0.0126 0.020 0.0157 0.001 0.0084
LatinX 0.009 0.0213 0.020 0.0246 0.001 0.0147
Multi 0.009 0.0103 0.020 0.0104 0.001 0.0086
Other 0.009 0.0065 0.020 0.0042 0.001 0.0065
White 0.009 0.0229 0.020 0.0271 0.001 0.0134
Table 6.  Results for the CFR using $ R_t(n) $ priors taken from piece-wise assimilation first assuming a CFR of 2% for all populations
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=89 $ Prior, $ \sigma=0.002 $ Post, $ \chi^2=41 $
Asian 0.020 0.0282 0.020 0.0199
Black 0.020 0.0337 0.020 0.0199
LatinX 0.020 0.0317 0.020 0.0200
Multi 0.020 0.0316 0.020 0.0202
Other 0.020 0.0299 0.020 0.0204
White 0.020 0.0259 0.020 0.0195
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=89 $ Prior, $ \sigma=0.002 $ Post, $ \chi^2=41 $
Asian 0.020 0.0282 0.020 0.0199
Black 0.020 0.0337 0.020 0.0199
LatinX 0.020 0.0317 0.020 0.0200
Multi 0.020 0.0316 0.020 0.0202
Other 0.020 0.0299 0.020 0.0204
White 0.020 0.0259 0.020 0.0195
Table 7.  Results for the CFR assuming a CFR of 2% for only the Black Group
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=302 $ Prior, $ \sigma=.1x $ Post, $ \chi^2=38 $ Prior, $ \sigma=0.05 $ $ \chi^2=83 $
Asian 0.0090 0.0101 0.0090 0.0091 0.0090 0.0249
Black 0.0200 0.0226 0.0200 0.0201 0.0200 0.0371
LatinX 0.0090 0.0211 0.0090 0.0092 0.0090 0.0299
Multi 0.0090 0.0097 0.0090 0.0092 0.0090 0.0285
Other 0.0090 0.0053 0.0090 0.0093 0.0090 0.0234
White 0.0090 0.0248 0.0090 0.0090 0.0090 0.0256
Population Prior, $ \sigma=0.05 $ Post, $ \chi^2=302 $ Prior, $ \sigma=.1x $ Post, $ \chi^2=38 $ Prior, $ \sigma=0.05 $ $ \chi^2=83 $
Asian 0.0090 0.0101 0.0090 0.0091 0.0090 0.0249
Black 0.0200 0.0226 0.0200 0.0201 0.0200 0.0371
LatinX 0.0090 0.0211 0.0090 0.0092 0.0090 0.0299
Multi 0.0090 0.0097 0.0090 0.0092 0.0090 0.0285
Other 0.0090 0.0053 0.0090 0.0093 0.0090 0.0234
White 0.0090 0.0248 0.0090 0.0090 0.0090 0.0256
Table 4.  CFR estimates coming from the run presented in Section 4.2.6
Population Prior, $ \sigma=0.009 $ Post, $ \chi^2=31 $
Asian 0.0900 0.0089
Black 0.0900 0.0100
LatinX 0.0900 0.0090
Multi 0.0900 0.0093
Other 0.0900 0.0094
White 0.0900 0.0094
Population Prior, $ \sigma=0.009 $ Post, $ \chi^2=31 $
Asian 0.0900 0.0089
Black 0.0900 0.0100
LatinX 0.0900 0.0090
Multi 0.0900 0.0093
Other 0.0900 0.0094
White 0.0900 0.0094
Table 8.  The table gives a set of first-guess model parameters. As we could not find scientific estimates of these parameters, we set their values based on available information from the internet and initial model-tuning experiments. We leave it to the data assimilation system to fine-tune the parameter values
Parameter First guess Description
$ \tau_ \rm{inc} $ 5.5 Incubation period
$ \tau_ \rm{inf} $ 3.8 Infection time
$ \tau_ \rm{recm} $ 14.0 Recovery time mild cases
$ \tau_ \rm{recs} $ 5.0 Recovery time severe cases
$ \tau_ \rm{hosp} $ 6.0 Time until hospitalization
$ \tau_ \rm{death} $ 16.0 Time until death
$ p_ \mathrm{f} $ 0.009 Case fatality rate
$ p_ \mathrm{s} $ 0.039 Hospitalization rate (severe cases)
$ p_ \mathrm{h} $ 0.4 Fraction of fatally ill going to hospital
Parameter First guess Description
$ \tau_ \rm{inc} $ 5.5 Incubation period
$ \tau_ \rm{inf} $ 3.8 Infection time
$ \tau_ \rm{recm} $ 14.0 Recovery time mild cases
$ \tau_ \rm{recs} $ 5.0 Recovery time severe cases
$ \tau_ \rm{hosp} $ 6.0 Time until hospitalization
$ \tau_ \rm{death} $ 16.0 Time until death
$ p_ \mathrm{f} $ 0.009 Case fatality rate
$ p_ \mathrm{s} $ 0.039 Hospitalization rate (severe cases)
$ p_ \mathrm{h} $ 0.4 Fraction of fatally ill going to hospital
Table 9.  The $ p $-numbers indicate the fraction of sick people in an age group ending up with mild symptoms, severe symptoms (hospitalized), and fatal infection
Age group 1 2 3 4 5 6 7 8 9 10 11
Age range 0–5 6–12 13–19 20–29 30–39 40–49 50–59 60–69 70–79 80–89 90–105
Population 351159 451246 446344 711752 730547 723663 703830 582495 435834 185480 45230
p–mild 1.0000 1.0000 0.9998 0.9913 0.9759 0.9686 0.9369 0.9008 0.8465 0.8183 0.8183
p–severe 0.0000 0.0000 0.0002 0.0078 0.0232 0.0295 0.0570 0.0823 0.1160 0.1160 0.1160
p–fatal 0.0000 0.0000 0.0000 0.0009 0.0009 0.0019 0.0061 0.0169 0.0375 0.0656 0.0656
Age group 1 2 3 4 5 6 7 8 9 10 11
Age range 0–5 6–12 13–19 20–29 30–39 40–49 50–59 60–69 70–79 80–89 90–105
Population 351159 451246 446344 711752 730547 723663 703830 582495 435834 185480 45230
p–mild 1.0000 1.0000 0.9998 0.9913 0.9759 0.9686 0.9369 0.9008 0.8465 0.8183 0.8183
p–severe 0.0000 0.0000 0.0002 0.0078 0.0232 0.0295 0.0570 0.0823 0.1160 0.1160 0.1160
p–fatal 0.0000 0.0000 0.0000 0.0009 0.0009 0.0019 0.0061 0.0169 0.0375 0.0656 0.0656
[1]

Geir Evensen, Javier Amezcua, Marc Bocquet, Alberto Carrassi, Alban Farchi, Alison Fowler, Pieter L. Houtekamer, Christopher K. Jones, Rafael J. de Moraes, Manuel Pulido, Christian Sampson, Femke C. Vossepoel. An international initiative of predicting the SARS-CoV-2 pandemic using ensemble data assimilation. Foundations of Data Science, 2021, 3 (3) : 413-477. doi: 10.3934/fods.2021001

[2]

Hailiang Liu, Xuping Tian. Data-driven optimal control of a seir model for COVID-19. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021093

[3]

Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170

[4]

Jorge Rebaza. On a model of COVID-19 dynamics. Electronic Research Archive, 2021, 29 (2) : 2129-2140. doi: 10.3934/era.2020108

[5]

Tailei Zhang, Zhimin Li. Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021088

[6]

Tao Zheng, Yantao Luo, Xinran Zhou, Long Zhang, Zhidong Teng. Spatial dynamic analysis for COVID-19 epidemic model with diffusion and Beddington-DeAngelis type incidence. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021154

[7]

Emiliano Alvarez, Juan Gabriel Brida, Lucía Rosich, Erick Limas. Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021026

[8]

Jiangqi Wu, Linjie Wen, Jinglai Li. Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021045

[9]

Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks. The estimation of the effective reproductive number from disease outbreak data. Mathematical Biosciences & Engineering, 2009, 6 (2) : 261-282. doi: 10.3934/mbe.2009.6.261

[10]

Azmy S. Ackleh, Jeremy J. Thibodeaux. Parameter estimation in a structured erythropoiesis model. Mathematical Biosciences & Engineering, 2008, 5 (4) : 601-616. doi: 10.3934/mbe.2008.5.601

[11]

Débora A. F. Albanez, Maicon J. Benvenutti. Continuous data assimilation algorithm for simplified Bardina model. Evolution Equations & Control Theory, 2018, 7 (1) : 33-52. doi: 10.3934/eect.2018002

[12]

John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021, 8 (3) : 167-188. doi: 10.3934/jdg.2021004

[13]

Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd. Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 553-576. doi: 10.3934/mbe.2012.9.553

[14]

Zhiting Xu. Traveling waves in an SEIR epidemic model with the variable total population. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3723-3742. doi: 10.3934/dcdsb.2016118

[15]

Fred Brauer. A model for an SI disease in an age - structured population. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257

[16]

Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 2823-2835. doi: 10.3934/dcdss.2020464

[17]

Jinliang Wang, Hongying Shu. Global analysis on a class of multi-group SEIR model with latency and relapse. Mathematical Biosciences & Engineering, 2016, 13 (1) : 209-225. doi: 10.3934/mbe.2016.13.209

[18]

Gianni Gilioli, Sara Pasquali, Fabrizio Ruggeri. Nonlinear functional response parameter estimation in a stochastic predator-prey model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 75-96. doi: 10.3934/mbe.2012.9.75

[19]

Blaise Faugeras, Olivier Maury. An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter estimation procedure: Application to the Indian Ocean skipjack tuna fishery. Mathematical Biosciences & Engineering, 2005, 2 (4) : 719-741. doi: 10.3934/mbe.2005.2.719

[20]

Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1735-1757. doi: 10.3934/dcdsb.2015.20.1735

 Impact Factor: 

Article outline

Figures and Tables

[Back to Top]