Optimal control when there is uncertainty.

<p>(a) Epidemic impact κ_<i>E</i> (total number of hosts lost to disease or control) as a function of the cull radius, <i>L</i>. The optimum value of <i>L</i> depends on the percentile of the distribution of κ_<i>E</i> that is being optimised (e.g. the optimum <i>L</i> would be 159m if the objective were to minimise median κ_<i>E</i>, whereas it would be 194m if minimising κ_<i>E</i> on the 95^th percentile). The shape of the distribution of κ_<i>E</i> varies with <i>L</i> (insets A to F; distributions renormalized to the same height by scaling all distributions relative to the largest value in each). (b) Risk of failure. Given a notion of “acceptable risk” (i.e. a value of Ω, the threshold κ_<i>E</i> as a percentage of the total population), the probability of failing to achieve κ_<i>E</i> < Ω is shown. Dotted line marks radii with < 10% risk of failure for Ω = 20% (range 122m < <i>L</i> < 329m). (c) Effect of the initial level of infection, E₀, on the response of median κ_<i>E</i> to <i>L</i> (dots show minimum median κ_<i>E</i> for each E₀). (d) and (e) Effect of the scale of dispersal (<i>α</i>) and rate of infection (<i>β</i>) on the optimal <i>L</i> (shown in d) and median κ_<i>E</i> at optimal <i>L</i> to optimise median κ_<i>E</i> (shown in e). The white dots on (d) and (e) indicate the default values of <i>α</i> and <i>β</i>; the white squares show the values of <i>α</i> and <i>β</i> fitted by Cook <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref024" target="_blank">24</a>] (and used in the studies of Parnell <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref011" target="_blank">11</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.ref012" target="_blank">12</a>]) <i>cf</i>. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004211#pcbi.1004211.s003" target="_blank">S3 Text</a>.