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Using early detection data to estimate the date of emergence of an epidemic outbreak

Fig 5

Model diagram.

(A) We model infectious disease transmission (dark blue elements) starting from a single infectious individual (full dark blue dot), using a general branching process. The generation time of secondary infections, {t_i+1 − t_i}_i=0,1,…, follows a Gamma distribution (shown in orange, above the first transmission event). In addition, we model the detection of infected individuals (light blue elements), which yields the time series of observed cases, , with M ≥ N. The number of cases are aggregated daily. Days are denoted by and depicted by alternating gray and white bands. Our algorithm stops the day at which the N^th case is observed, d_K, but our analyses deal with the set of all cases detected on day d_K, , where y_j denotes the j^th detected infection (i.e., the j^th case). (B) Resulting epidemic curve (cases per day). Our model is calibrated so that the simulated epidemic curve, , reproduces the observed number of cases per day. The main outcome of our model is the number of days elapsed between the first infection and the N^th observed case, d_K. NB. The time scale in the figure is not representative of our simulations: infection and detection delays in the simulations usually span multiple days.

doi: https://doi.org/10.1371/journal.pcbi.1011934.g005