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FoI and Age-Dependence

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Epidemics

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Notes

  1. 1.

    The theoretical FoI is model specific, so more complicated models may have more complicated FoIs. The FoI for the Ebola SEIHFR model of Sect. 3.10, for example, is given by rate ① in Fig. 3.9.

  2. 2.

    Liu et al. (1986) proposed that spatial clustering can be modeled by a transmission term βS p I q∕N, with p and q between zero and one.

  3. 3.

    The notion of a critical host density is discussed in more detail in Sect. 10.7.

  4. 4.

    A thin-plate spline is a spline-based technique that produces smooth surfaces in 2 (or higher) dimensions (Wood, 2003).

  5. 5.

    Recall that the with(as.list(…)) allows evaluation of the equations using the definitions in the parameters vector and % ∗ % denotes matrix multiplication.

  6. 6.

    The tiny non-zero fraction of initials in the R group in the code is because integrating the model in log-coordinates for numerical stability requires non-zero state variables, so \(\log (0)=-\infty \) would break the numerical integrator.

  7. 7.

    This is another unfortunate case of notation conventions in different fields pertinent to infectious disease dynamics that adds confusion to the Greek alphabet soup; this text generally adheres to mathematical epidemiology conventions for which α is commonly used for rate of infection-induced mortality, but in mathematical demography α ij conventionally refers to the i’th row and j’th column of the Leslie matrix.

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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). FoI and Age-Dependence. In: Epidemics. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-031-12056-5_4

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