burnout is an R package for calculating the probability of epidemic burnout (or persistence) after a major outbreak. It was used to create the figures in

Parsons TL, Bolker BM, Dushoff J, Earn DJD (2024), "The probability of epidemic burnout in the stochastic SIR model with vital dynamics", PNAS, Volume: 121, Issue: 5, DOI: 10.1073/pnas.2313708120

The burnout package requires R ≥ 4.2.0 in order for the documentation to be displayed as desired. As mentioned here, 4.2.0 automatically supports KaTeX and MathJax, which I use liberally in roxygen documentation.

The remainder of this file currently contains notes for the authors. We will clean this up when time permits.

• LaTeX issues: \\mathscr (mathrsfs package?, Debugging: R CMD Rdconv man/burnout.Rd

R CMD Rd2pdf burnout/man/burnout.Rd

generating graphs from Parsons et al (2024)

Generate the analytical curves in Figure 3 via

example(plot_P1)

Generate Figures B1 and B2 via

example(plot_x_in)

Note that the green/blue curves (i.e., crude/better approximations of peak prevalence ymax) in Todd's plots correspond to dotted/solid curves in this plot.

comparing approximations

The function compare_funs creates a data frame with values of two functions of R0 and epsilon at a grid of points. It returns an object of class compare_funs, for which there is a plot method. So, for example, the following compares the exact and approximate expressions for Kendalls's q:

cf <- compare_funs()
plot(cf)

To compare the crude and better approximations of xin, use

cxinc <- compare_funs(x_in, x_in_crude, Rmax=20)
plot(cxinc)

In the above plot (with Rmax = 20) the bottom two panels (for epsilon = 0.01 and 0.1) correspond to Figure B1 in the paper.

To compare the approximate and exact xin, use

cxine <- compare_funs(x_in, x_in_exact)
plot(cxine)

or, to look a little more closely use, for example,

cxine <- compare_funs(x_in, x_in_exact, Rmax=8, epsilon=0.01)
plot(cxine)

To compare van Herwaarden's (1997) approximation to ours:

ch <- compare_funs(P1_prob, P1_prob_vanH)
plot(ch)

_Note, however, that the above works only because of a try catch inside vanH_prob. We actually need to resolve this._

A better test is to compare the burnout probabilities (conditional on not fizzling), as opposed to the persistence probabiities, because P1 is derived from the burnout probability identically in all cases. The formulae that are different are the components from burning out conditional on not fizzling:

cb <- compare_funs(burnout_prob, burnout_prob_vanH)
plot(cb)

To compare van Meerson and Sasorov's (2009) approximation to ours:

cms <- compare_funs(P1_prob, P1_prob_MS)
plot(cp)