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A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process

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Predicting Pandemics in a Globally Connected World, Volume 1

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Abstract

This chapter presents a novel point process model for COVID-19 transmission—the multivariate recursive Hawkes process, which is an extension of the recursive Hawkes model to the multivariate case. Equivalently the model can be viewed as an extension of the multivariate Hawkes model to allow for varying productivity as in the recursive model. Several theoretical properties of this process are stated and proved, including the existence of the multivariate recursive counting process and formulas for the mean and variance. EM-based algorithms are explored for estimating parameters of parametric and semi-parametric forms of the model. Additionally, an algorithm is presented to reconstruct the process from imprecise event times. The performance of the algorithms on both synthetic and real COVID-19 data sets is illustrated through several experiments.

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Notes

  1. 1.

    https://github.com/wispcarey/Bohan_MRHP.

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Acknowledgment

This work is supported by NSF grants DMS-2027277, DMS-1737770, DMS-2124313, and DMS-2027438 and Simons Foundation Math +  X Investigator Award # 510776.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, USA

    Bohan Chen & Andrea L. Bertozzi

  2. Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA

    Pujan Shrestha

  3. Department of Computer Science, Boston College, Boston, MA, USA

    George Mohler

  4. Department of Statistics, University of California, Los Angeles, Los Angeles, CA, USA

    Frederic Schoenberg

Authors
  1. Bohan Chen
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  2. Pujan Shrestha
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  3. Andrea L. Bertozzi
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  4. George Mohler
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  5. Frederic Schoenberg
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Corresponding author

Correspondence to Andrea L. Bertozzi .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy

    Nicola Bellomo

  2. School of Mathematics and Statistics, University of St. Andrews, St. Andrews, UK

    Mark A. J. Chaplain

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Chen, B., Shrestha, P., Bertozzi, A.L., Mohler, G., Schoenberg, F. (2022). A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process. In: Bellomo, N., Chaplain, M.A.J. (eds) Predicting Pandemics in a Globally Connected World, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-96562-4_5

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