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Using a partial differential equation with Google Mobility data to predict COVID-19 in Arizona

1 School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069, USA
2 School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA

Special Issues: Modeling the Biological, Epidemiological, Immunological, Molecular, Virological Aspects of COVID-19

The outbreak of COVID-19 disrupts the life of many people in the world. The state of Arizona in the U.S. emerges as one of the country’s newest COVID-19 hot spots. Accurate forecasting for COVID-19 cases will help governments to implement necessary measures and convince more people to take personal precautions to combat the virus. It is difficult to accurately predict the COVID- 19 cases due to many human factors involved. This paper aims to provide a forecasting model for COVID-19 cases with the help of human activity data from the Google Community Mobility Reports. To achieve this goal, a specific partial differential equation (PDE) is developed and validated with the COVID-19 data from the New York Times at the county level in the state of Arizona in the U.S. The proposed model describes the combined effects of transboundary spread among county clusters in Arizona and human activities on the transmission of COVID-19. The results show that the prediction accuracy of this model is well acceptable (above 94%). Furthermore, we study the effectiveness of personal precautions such as wearing face masks and practicing social distancing on COVID-19 cases at the local level. The localized analytical results can be used to help to slow the spread of COVID- 19 in Arizona. To the best of our knowledge, this work is the first attempt to apply PDE models on COVID-19 prediction with the Google Community Mobility Reports.
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Keywords COVID-19; partial differential equation; prediction; social distancing; Google Community Mobility Reports

Citation: Haiyan Wang, Nao Yamamoto. Using a partial differential equation with Google Mobility data to predict COVID-19 in Arizona. Mathematical Biosciences and Engineering, 2020, 17(5): 4891-4904. doi: 10.3934/mbe.2020266


  • 1. Arizona Department of Health Services, Confirmed COVID-19 Cases by Day, 2020. Available from: https://www.azdhs.gov/preparedness/epidemiology-disease-control/infectious-disease-epidemiology/covid-19/dashboards/index.php.
  • 2. S. He, S. Tang, L. Rong, A discrete stochastic model of the COVID-19 outbreak: Forecast and control, Math. Biosci. Eng., 17 (2020), 2792-2804.
  • 3. M. T. Li, G. Q. Sun, J. Zhang, Y. Zhao, X. Pei, L. Li, et al., Analysis of COVID-19 transmission in Shanxi Province with discrete time imported cases, Math. Biosci. Eng., 17 (2020), 3710-3720.
  • 4. L. Wang, J. Wang, H. Zhao, Y. Shi, K. Wang, P. Wu, et al., Modelling and assessing the effects of medical resources on transmission of novel coronavirus (COVID-19) in Wuhan, China, Math. Biosci. Eng., 17 (2020), 2936-2949.
  • 5. Y. Huang, L. Yang, H. Dai, F. Tian, K. Chen, Epidemic situation and forecasting of COVID-19 in and outside China, Bull. World Health Organ., (2020). E-pub: 16 March 2020.
  • 6. S. Lai, N. W. Ruktanonchai, L. Zhou, O. Prosper, W. Luo, J. R. Floyd, et al., Effect of nonpharmaceutical interventions to contain COVID-19 in China, Nature, (2020). https://doi.org/10.1038/s41586-020-2293-x.
  • 7. R. Omori, R. Matsuyama, Y. Nakata, Does susceptibility to novel coronavirus (COVID-19) infection differ by age?: Insights from mathematical modelling, medRxiv, (2020). https://doi.org/10.1101/2020.06.08.20126003.
  • 8. Z. Yang, Z. Zeng, K. Wang, S. Wong, W. Liang, M. Zanin, et al., Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions, J. Thorac. Dis., 12 (2020), 165-174.
  • 9. K. Prem, Y. Liu, T. W. Russell, A. J. Kucharski, R. M. Eggo, N. Davies, The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study, Lancet Public Health, 5 (2020), e261-70.
  • 10. B. S. Pujari, S. M. Shekatkar, Multi-city modeling of epidemics using spatial networks: Application to 2019-nCov (COVID-19) coronavirus in India, medRxiv, (2020). https://doi.org/10.1101/2020.03.13.20035386.
  • 11. F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical Models in Epidemiology, Springer, (2019).
  • 12. E. E. Holmes, M. A. Lewis, J. E. Banks, R. R. Veit, Partial differential equations in ecology: spatial interactions and population dynamics, Ecology, 75 (1994), 17-29.
  • 13. Y. Wang, K. Xu, Y. Kang, H. Wang, F. Wang, A. Avram, Regional influenza prediction with sampling Twitter data and PDE model, Int. J. Environ. Res. Public Health, 17 (2020), 678.
  • 14. M. Zhu, X. Guo, Z. Lin, The risk index for an SIR epidemic model and spatial spreading of the infectious disease, Math. Biosci. Eng., 14 (2017), 1565-1583.
  • 15. H. Wang, F. Wang, K. Xu, Modeling information diffusion in online social networks with partial differential equations, Springer, 2020. https://doi.org/10.1007/978-3-030-38852-2.
  • 16. F. Wang, H. Wang, K. Xu, R. Raymond, J. Chon, S. Fuller, et al., Regional level influenza study with geo-tagged Twitter data, J. Med. Syst., 40 (2016), 189.
  • 17. Google, Google COVID-19 Community Mobility Reports, Google. https://www.google.com/covid19/mobility/.
  • 18. N. Picchiotti, M. Salvioli, E. Zanardini, F. Missale, COVID-19 pandemic: a mobility-dependent SEIR model with undetected cases in Italy, Europe and US, arXiv:2005.08882. https://arxiv.org/abs/2005.08882.
  • 19. R. Abouk, B. Heydari, The immediate effect of COVID-19 policies on social distancing behavior in the United States, medRxiv, 2020.04.07.20057356. https://doi.org/10.1101/2020.04.07.20057356.
  • 20. Z. Vokó, J. G. Pitter, The effect of social distance measures on COVID-19 epidemics in Europe: an interrupted time series analysis, GeroScience, https://doi.org/10.1007/s11357-020-00205-0.
  • 21. J. D. Murray, Mathematical biology. I. an introduction, Photosynthetica, 40 (2002), 414.
  • 22. A. Friedman, Partial differential equations, Courier Dover Publications, 2008.
  • 23. I. V. Oseledets, Tensor-train decomposition, SIAM J. Sci. Comput., 33 (2011), 2295-2317.
  • 24. J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, Convergence properties of the nelder-mead simplex method in low dimensions, SIAM J. Optim., 9 (1998), 112-147.


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