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Spatial Dynamics

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Epidemics

Part of the book series: Use R! ((USE R))

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Abstract

Space adds an additional axis to the richness of infectious disease dynamics. For example, Gog et al. (2014) detailed the diffusive nature of the spread of influenza A/H1N1pdv and Lau et al. (2017) characterized the geographic spread of the West African 2014–2015 Ebola outbreak. Walsh et al. (2005) calculated that Ebola was spreading through gorilla and chimpanzee populations at 50 km/year. Moreover, Grenfell and Harwood (1997) and Keeling et al. (2004) outlined how spatial spread may permit long-term persistence through metapopulation dynamics.

This chapter uses the following R packages: ncf, animation and plotly.

A five minute epidemics MOOC on spatial spread is: https://www.youtube.com/watch?v=WPjsAdyD1Gg

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Notes

  1. 1.

    As discussed in Sect. 9.4 these two models are not nested in the sense that one model is a simpler version of the other so formal likelihood ratio test does not apply.

  2. 2.

    Just like the chain-binomial model in Sects. 3.4 and 3.5, the spatial logistic can be used both as a statistical method and as a stochastic simulator.

  3. 3.

    This is closely related to Tilman’s (1976) R ∗ theory of competitive dominance discussed in Sects. 3.1 and 3.12.

  4. 4.

    The name refers to how the most stylized of these models assumes a lattice (checker board) of locations at which local numbers change from one generation to the next according to some “map**” rule of onward local change such as the discrete logistic, the Nicholson-Baily model (see Chap. 16) or, in this case, a discrete-time seasonally forced SI model, followed by spatial redistribution via some spatial coupling rule.

  5. 5.

    The system() function in R passes the convert and rm calls to the command line. A web-optimized version of the animated GIF can be viewed on https://git.io/JMnHk. While not using base R syntax the plotly package is very effective for generating browser-rendered animations. An example can be found in the nbspat.app shinyApp in Chap. 16.

  6. 6.

    Seabloom et al. (2005) provide similar calculations for spatial plant competition models.

  7. 7.

    Note that this formulation assumes that spatial transmission does not dilute local transmission. Keeling and Rohani (2002) provide a discussion of this issue. Section 15.7 also considers a model for which spatial transmission dilutes local transmission.

  8. 8.

    Viboud et al. (2006) showed that the commuter flows has a fatter tailed kernel (Sect. 12.2) than predicted by this gravity model which we, for expedience, ignore.

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  1. Center for Infectious Disease Dynamics, Pennsylvania State University, University Park, PA, USA

    Ottar Bjørnstad

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Bjørnstad, O. (2023). Spatial Dynamics. In: Epidemics. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-031-12056-5_12

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