Key data for outbreak evaluation: building on the Ebola experience

Cori, Anne; Donnelly, Christl A.; Dorigatti, Ilaria; Ferguson, Neil M.; Fraser, Christophe; Garske, Tini; Jombart, Thibaut; Nedjati-Gilani, Gemma; Nouvellet, Pierre; Riley, Steven; Van Kerkhove, Maria D.; Mills, Harriet L.; Blake, Isobel M.

(ii) Short-and long-term incidence projections Short-term impact of an outbreak can be assessed by predicting the number of cases that will arise in the next few days or weeks. This is particularly relevant for evaluation of immediate health-care capacity needs. Projections of future incidence and estimates of the doubling time (the time taken for the incidence to double) can be obtained by extrapolating the early time series of reported cases either obtained from aggregated surveillance data or calculated from individual records [31] . These projections typically rely on the assumption that incidence initially grows exponentially [31] . They are subject to uncertainty, which increases the further one looks into the future. Quantifying and appropriately reporting such uncertainty and underlying assumptions are crucial [22, 25, 32, 33] . Overstating uncertainty can lead to inappropriately pessimistic projections, which may in turn be detrimental to the control of the outbreak [34] . On the other hand, understating uncertainty prevents policymakers from making decisions based on the whole spectrum of possible impacts. Some studies have already discussed how to find the balance between these two extremes [35 -37] . Here, we propose two simple rules of thumb for projecting case numbers. First, projections should not be made for more than two or three generations of cases into the future. Second, central projections should be shown together with lower and upper bounds. In the future, the modelling community should agree on guidelines for reporting epidemic projections, as are already in place for reporting experimental studies [38] . A number of factors can lead to incidence not growing exponentially. In particular, this happens once herd immunity accumulates, if population behaviour changes or as a result of the implementation of interventions. Dynamic transmission models, which account for saturation effects, can be used to assess the long-term impact of the outbreak such as predicting the timing and magnitude of the epidemic peak or the attack rate (final proportion of population infected) [39, 40] . However, these models are hard to parametrize as they require information on population size and immunity, interventions (if any) and potential behavioural changes over time, all of which may be subject to uncertainty [41, 42] . We discuss these issues in more detail in §3. Projecting longer term is likely to be associated with a large degree of uncertainty and these projections may be more useful for evaluating qualitative trends and evaluating intervention choices rather than predicting exact case numbers.