Fig 1.
Incorrect estimation of the probability of a major outbreak.
The number of presymptomatic infected individuals is estimated (giving a distribution of possible values), and these values are used as initial conditions in forward simulations to build a point estimate of the probability of a major outbreak (bottom left—here, the estimated probability of a major outbreak is 0.55). However, the number of presymptomatic infected individuals actually takes a single value, which can be used in forward simulations to determine the true probability of a major outbreak (bottom right—here, the true probability of a major outbreak is 0.78). The underlying dataset is simulated using the SEIR model, and the predicted future behaviors shown are generated using 100,000 forward simulations of the model.
Fig 2.
Uncertainty in the probability of a major outbreak when presymptomatic infection cannot be detected.
A. Given the true probability of a major outbreak, what point estimate for the estimated probability of a major outbreak might be obtained? (100,000 simulated datasets using the SEIR model for each true probability). For clarity, true probabilities greater than 0.97 are classified into bins of size 0.01. B. How does the true probability of a major outbreak vary between outbreaks with the same point estimate for the probability of a major outbreak? Estimated probabilities are classified into bins of size 0.1 (100,000 simulated datasets per bin). Circle areas are proportional to the number of outbreaks at each true probability, normalized for each bin of estimated probabilities of a major outbreak, so that the sum of the areas of the circles along each horizontal line is constant.
Fig 3.
Error in estimating the probability of a major outbreak using the SEIR model when asymptomatic individuals are tested for infection.
A. The mean error in the probability of a major outbreak, as a function of the percentage of asymptomatic individuals tested and the probability that presymptomatic infection is correctly identified (calculated from 10,000 simulations for each (percentage, pd) pair). B. Variation in estimates of the probability of a major outbreak when 95% of asymptomatic individuals are tested and the test is perfectly reliable. C. Variation in estimates of the probability of a major outbreak when 50% of asymptomatic individuals are tested and presymptomatic infection is correctly identified 50% of the time.
Fig 4.
Estimating the probability of a major outbreak when incubation and latent periods are not identical.
A. Symptoms occur before infectiousness. B. Symptoms occur after infectiousness. In B, the number of presymptomatic infected individuals is estimated using reversible jump Markov chain Monte Carlo [48]. In the boxplots in A, for clarity, true probabilities greater than 0.98 are classified into bins of size 0.01, and in B, true probabilities greater than 0.8 are classified into bins of size 0.01.