R0 function - RDocumentation (2024)

The S3 generic function R0 defined in package surveillance is intended tocompute reproduction numbers from fitted epidemic models.The package currently defines a method for the "twinstim" class, whichcomputes expected numbers of infections caused by infected individuals depending on the event typeand marks attached to the individual, which contribute to the infection pressurein the epidemic predictor of that class.There is also a method for simulated "epidataCS"(just a wrapper for the "twinstim"-method).

For the R0 methods, a numeric vector of estimated reproduction numbers from the fitted model object corresponding to the rows of newevents (if supplied) or the original fitted events including events of the prehistory.

For simpleR0, a single number (see details).

For the "twinstim" class, the individual-specific expectednumber \(\mu_j\) of infections caused by individual (event) \(j\)inside its theoretical (untrimmed) spatio-temporal range of interactiongiven by its eps.t (\(\epsilon\)) and eps.s(\(\delta\)) values is defined as follows (cf. Meyer et al, 2012):$$\mu_j = e^{\eta_j} \cdot \int_{b(\bold{0},\delta)} f(\bold{s}) d\bold{s} \cdot \int_0^\epsilon g(t) dt .$$Here, \(b(\bold{0},\delta)\) denotes the disc centred at (0,0)' withradius \(\delta\), \(\eta_j\) is the epidemic linear predictor,\(g(t)\) is the temporal interaction function, and \(f(\bold{s})\)is the spatial interaction function. For a type-specifictwinstim, there is an additional factor for the number of eventtypes which can be infected by the type of event \(j\) and theinteraction functions may be type-specific as well.

Alternatively to the equation above,the trimmed (observed) reproduction numbersare obtain by integrating over the observed infectious domains of theindividuals, i.e. integrate \(f\) over the intersection of theinfluence region with the observation region W(i.e. over \(\{ W \cap b(\bold{s}_j,\delta) \} - \bold{s}_j\))and \(g\) over the intersection of the observed infectious period withthe observation period \((t_0;T]\) (i.e. over\((0; \min(T-t_j,\epsilon)]\)).

The function simpleR0 computes$$\exp(\eta) \cdot \int_{b(\bold{0},\delta)} f(\bold{s}) d\bold{s} \cdot \int_0^{\epsilon} g(t) dt ,$$where \(\eta\) defaults to \(\gamma_0\) disregarding any epidemiceffects of types and marks. It is thus onlysuitable for simple epidemic twinstim models withepidemic = ~1, a diagonal (or secondary diagonal) qmatrix,and type-invariant interaction functions.simpleR0 mainly exists for use by epitest.

(Numerical) Integration is performed exactly as during the fitting ofobject, for instance object$control.siaf is queried ifnecessary.

Meyer, S., Elias, J. and Höhle, M. (2012): A space-time conditional intensity model for invasive meningococcal disease occurrence. Biometrics, 68, 607-616. tools:::Rd_expr_doi("10.1111/j.1541-0420.2011.01684.x")