Statistical Science

Self-Exciting Point Processes: Infections and Implementations

Sebastian Meyer

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This is a contribution to the discussion of Reinhart’s “Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications” [Statist. Sci. 33 (2018)], which synthesizes developments from various research fields. Here, I discuss some experiences from modeling the spread of infectious diseases. Furthermore, I try to complement the review with regard to the availability of software for the described models, which I think is essential in “paving the way for new uses.”

Article information

Statist. Sci., Volume 33, Number 3 (2018), 327-329.

First available in Project Euclid: 13 August 2018

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Spatio-temporal modeling infectious disease epidemiology statistical software


Meyer, Sebastian. Self-Exciting Point Processes: Infections and Implementations. Statist. Sci. 33 (2018), no. 3, 327--329. doi:10.1214/18-STS653.

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  • Adelfio, G. and Chiodi, M. (2015). FLP estimation of semi-parametric models for space–time point processes and diagnostic tools. Spat. Stat. 14 119–132.
  • Aldrin, M., Huseby, R. B. and Jansen, P. A. (2015). Space–time modelling of the spread of pancreas disease (PD) within and between Norwegian marine salmonid farms. Preventive Veterinary Medicine 121 132–141.
  • Baddeley, A. and Turner, R. (2005). spatstat: An R package for analyzing spatial point patterns. J. Stat. Softw. 12 1–42.
  • Brockmann, D., Hufnagel, L. and Geisel, T. (2006). The scaling laws of human travel. Nature 439 462–465.
  • Diggle, P. J. (2006). Spatio-temporal point processes, partial likelihood, foot and mouth disease. Stat. Methods Med. Res. 15 325–336.
  • Gibbons, C. L., Mangen, M.-J. J., Plass, D., Havelaar, A. H., Brooke, R. J., Kramarz, P., Peterson, K. L., Stuurman, A. L., Cassini, A., Fèvre, E. M. and Kretzschmar, M. E. (2014). Measuring underreporting and under-ascertainment in infectious disease datasets: A comparison of methods. BMC Public Health 14 1–17.
  • Harte, D. (2010). PtProcess: An R package for modelling marked point processes indexed by time. J. Stat. Softw. 35 1–32.
  • Held, L. and Meyer, S. (2018). Forecasting based on surveillance data. In Handbook of Infectious Disease Data Analysis (L. Held, N. Hens, P. D. O’Neill and J. Wallinga, eds.) Chapman & Hall/CRC, Boca Raton, FL. To appear.
  • Höhle, M. (2009). Additive-multiplicative regression models for spatio-temporal epidemics. Biom. J. 51 961–978.
  • Höhle, M. (2016). Infectious disease modelling. In Handbook of Spatial Epidemiology (A. B. Lawson, S. Banerjee, R. P. Haining and M. D. Ugarte, eds.) 477–500. CRC Press, Boca Raton, FL.
  • Jalilian, A. (2018). ETAS: Modeling earthquake data using ETAS model. R package version 0.4.4, Comprehensive R Archive Network.
  • Kasahara, A., Yagi, Y. and Enescu, B. (2016). etas_solve: A robust program to estimate the ETAS model parameters. Seismological Research Letters 87 1143.
  • Lombardi, A. M. (2017). SEDA: A software package for the statistical earthquake data analysis. Sci. Rep. 7 44171.
  • Meyer, S., Elias, J. and Höhle, M. (2012). A space–time conditional intensity model for invasive meningococcal disease occurrence. Biometrics 68 607–616.
  • Meyer, S. and Held, L. (2014). Power-law models for infectious disease spread. Ann. Appl. Stat. 8 1612–1639.
  • Meyer, S., Held, L. and Höhle, M. (2017). Spatio-temporal analysis of epidemic phenomena using the R package surveillance. J. Stat. Softw. 77 1–55.
  • Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83 9–27.
  • Read, J. M., Lessler, J., Riley, S., Wang, S., Tan, L. J., Kwok, K. O., Guan, Y., Jiang, C. Q. and Cummings, D. A. T. (2014). Social mixing patterns in rural and urban areas of southern China. Proc. R. Soc. Lond., B Biol. Sci. 281.
  • Ross, G. J. (2017). bayesianETAS: Bayesian estimation of the ETAS model for earthquake occurrences. R package version 1.0.3, Comprehensive R Archive Network.
  • Scheel, I., Aldrin, M., Frigessi, A. and Jansen, P. A. (2007). A stochastic model for infectious salmon anemia (ISA) in Atlantic salmon farming. J. R. Soc. Interface 4 699–706.
  • Schrödle, B., Held, L. and Rue, H. (2012). Assessing the impact of a movement network on the spatiotemporal spread of infectious diseases. Biometrics 68 736–744.
  • Taylor, B., Davies, T., Rowlingson, B. and Diggle, P. (2013). Bayesian inference and data augmentation schemes for spatial, spatiotemporal and multivariate log-Gaussian Cox processes in R. J. Stat. Softw. 63 1–48.
  • The Institute of Statistical Mathematics (2016). SAPP: Statistical analysis of point processes. R package version 1.0.7, Comprehensive R Archive Network.

See also

  • Main article: A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications.