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A recursive point process model for infectious diseases

Author

Listed:
  • Frederic Paik Schoenberg

    (University of California)

  • Marc Hoffmann

    (PSL Research University, Université Paris-Dauphine)

  • Ryan J. Harrigan

    (University of California)

Abstract

We introduce a new type of point process model to describe the incidence of contagious diseases. The model incorporates the premise that when a disease occurs at low frequency in the population, such as in the primary stages of an outbreak, then anyone with the disease is likely to have a high rate of transmission to others, whereas when the disease is prevalent, the transmission rate is lower due to prevention measures and a relatively high percentage of previous exposure in the population. The model is said to be recursive, in the sense that the conditional intensity at any time depends on the productivity associated with previous points, and this productivity in turn depends on the conditional intensity at those points. Basic properties of the model are derived, estimation and simulation are discussed, and the recursive model is shown to fit well to California Rocky Mountain Spotted Fever data.

Suggested Citation

  • Frederic Paik Schoenberg & Marc Hoffmann & Ryan J. Harrigan, 2019. "A recursive point process model for infectious diseases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1271-1287, October.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0690-9
    DOI: 10.1007/s10463-018-0690-9
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    References listed on IDEAS

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    1. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. Yosihiko Ogata & Koichi Katsura & Masaharu Tanemura, 2003. "Modelling heterogeneous space–time occurrences of earthquakes and its residual analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 499-509, October.
    3. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    4. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    5. Kate E. Jones & Nikkita G. Patel & Marc A. Levy & Adam Storeygard & Deborah Balk & John L. Gittleman & Peter Daszak, 2008. "Global trends in emerging infectious diseases," Nature, Nature, vol. 451(7181), pages 990-993, February.
    6. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    7. Earvin Balderama & Frederic Paik Schoenberg & Erin Murray & Philip W. Rundel, 2012. "Application of Branching Models in the Study of Invasive Species," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 467-476, June.
    8. Frederic Schoenberg, 2006. "On Non-simple Marked Point Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 223-233, June.
    9. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
    10. Harte, David, 2010. "PtProcess: An R Package for Modelling Marked Point Processes Indexed by Time," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i08).
    11. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
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    Cited by:

    1. Sarita D. Lee & Andy A. Shen & Junhyung Park & Ryan J. Harrigan & Nicole A. Hoff & Anne W. Rimoin & Frederic Paik Schoenberg, 2022. "Comparison of prospective Hawkes and recursive point process models for Ebola in DRC," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 201-210, January.
    2. Frederic Paik Schoenberg, 2022. "Nonparametric estimation of variable productivity Hawkes processes," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    3. Racek, Daniel & Thurner, Paul & Kauermann, Goeran, 2024. "Integrating Spatio-temporal Diffusion into Statistical Forecasting Models of Armed Conflict via Non-parametric Smoothing," OSF Preprints q59dr, Center for Open Science.
    4. Grames, Eliza M. & Stepule, Piper L. & Herrick, Susan Z. & Ranelli, Benjamin T. & Elphick, Chris S., 2022. "Separating acoustic signal into underlying behaviors with self-exciting point process models," Ecological Modelling, Elsevier, vol. 468(C).
    5. Kieran Kalair & Colm Connaughton & Pierfrancesco Alaimo Di Loro, 2021. "A non‐parametric Hawkes process model of primary and secondary accidents on a UK smart motorway," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 80-97, January.

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