K - College of Natural Resources - University of California, Berkeley

(B) Proportion of cases causing 99 th -percentile SSEs, Ψ, compared with predicted Ψ
and 95% confidence intervals for Z~Poisson( ˆ ) (circles and dashed lines) and
Z~NegB( ˆ , ˆ ) (triangles and solid lines). Observed proportions (stars) were
R 0,mle
k mle
R 0,mle
calculated from (# SSEs)/(# cases), as shown; for Ebola HF, Ψobs=0 so the star is not
visible. Data from Table 1; smallpox 1,2,3 refer to data from Europe, Benin and
England, respectively. (C) Expected proportion of cases causing 99 th -percentile
SSEs, ΨR,k, for outbreaks with Z~NegB(R,k). Values of R were selected such that
Pr(Z≤Z (99) |Z~Poisson(R))=0.01 (see appendix A).
Figure 3
Disease invasion dynamics with different degrees of individual variation in
infectiousness. (A) Individual reproductive number ν is drawn from a gamma
distribution with mean R0 and shape parameter k. Probability density functions are
shown for seven gamma distributions with R0=1.5. (B) Probability of stochastic
extinction of an outbreak, q, versus population-average reproductive number R0,
following introduction of a single infected case, for k=0.01 (red), k=0.1 (blue), k=0.5
(green), k=1 (black), k=4 (cyan), kØ∞ (magenta). (C) Growth rate of simulated
outbreaks with R0=1.5 and one initial case, conditional on non-extinction. Boxes show
median and interquartile range of the first disease generation with 100 cases; whiskers
show 95-percentile range, and crosses show outliers. Percentages show the proportion
of 10,000 simulated outbreaks that reached the 100-case threshold (i.e. roughly 1-q).
121