Early Estimates of Monkeypox Incubation Period, Generation Time, and Reproduction Number, Italy, May–June 2022

We analyzed the first 255 PCR-confirmed cases of monkeypox in Italy in 2022. Preliminary estimates indicate mean incubation period of 9.1 (95% CI 6.5–10.9) days, mean generation time of 12.5 (95% CI 7.5–17.3) days, and reproduction number among men who have sex with men of 2.43 (95% CI 1.82–3.26).


Incubation Period
To compute the incubation period, we considered all monkeypox cases confirmed through July 8, 2022, with a known date of symptom onset and for which >1 of the following information was reported: • the latest day of exposure, as ascertained by contact tracing investigation (this information is available for 15 cases); • a history of travel to Canary Islands, together with the dates of sojourn (this information is available for 15 cases).
As a baseline, we thus considered a total of 30 confirmed cases with prior information on the possible date of exposure (Appendix Table 1).
We assumed that the incubation period is distributed as a gamma function and we estimated the shape (k) and scale parameters ( ) following a Bayesian approach similar to the one adopted in Miura et al.
(1), based on a Monte Carlo Markov Chain (MCMC) procedure and Metropolis-Hastings sampling. At each MCMC iteration: • we sampled 1 date of infection for each confirmed case, considering the information available for each subject. For cases with a known latest day of exposure, the date of infection was fixed to this value; for cases with a travel history to Canary Islands, the sampled date of infection was constrained to be between the date of departure to and return from Canary Islands.
• for each confirmed case, we computed the incubation periods as the difference between the date of symptom onset and the sampled date of infections.
• we sampled 1 value for the shape (k) and 1 value for the scale parameter ( ) of the gamma function.
• we compute the gamma likelihood of observing the computed incubation periods given parameters {k, } The resulting estimates of the parameters are reported in Appendix Table 2. The cumulative density function estimated for the incubation period is shown in Appendix Figure 1 along with the cumulative distribution of incubation periods associated to the parameter set with the maximum likelihood.
As sensitivity analyses, we estimated the incubation period by considering separately the 15 cases with a known latest date of exposure (sensitivity A) and the 15 cases with a history of travel to Canary Islands (sensitivity B).

Generation Time
The generation time is defined as the difference between the date of infection of a confirmed case and those of secondary cases. To estimate the generation time, we followed a MCMC procedure similar to the one used for the incubation period, by assuming a gamma distributed generation time. In the data, there were 16 identified infector-infectee pairs with known dates of symptom onset (Appendix Table 3). For 2 cases, an exact date of last exposure was identified during epidemiologic investigations and therefore assumed as infection date. For 1 case-patient who reported traveling to Canary Islands but had no other known exposure, we constrained the sampled infection date to be within the dates of departure to and return from Canary Islands. For other cases, the dates of infection were randomly sampled assuming that presymptomatic transmission is not possible (i.e., the date of infection for the secondary cases should always be greater or equal to the date of symptom onset of the infector). Dates of infection were sampled using as a uniform prior between values lying within the 95% CI of the incubation period estimated in the baseline analysis.
The obtained distribution of the generation time is reported in Appendix Figure 2, and the values are summarized in Appendix Table 4.

Reproduction number Rt
We computed the net reproduction number Rt for the monkeypox outbreak using the epidemic curve of cases by date of symptom onset and the estimated distribution of the generation time, by applying a standard statistical method based on the renewal equation. The posterior distribution of Rt can be computed by applying a MCMC algorithm to the following likelihood function: • P(k; λ) is the probability mass function of a Poisson distribution (i.e., the probability of observing k events if these events occur with rate λ).
• C(t) is the total daily number of new cases having symptom onset at time t; • I(t) is the total daily number of new cases that are not locally transmitted; • Rt is the net reproduction number at time t to be estimated; • φ(s) is the probability distribution density of the generation time discretized by day, evaluated at days s.
We considered 3 different assumptions for imported cases: 1) we considered only the case with earliest symptom onset as an imported case. This is a rather unrealistic hypothesis that can give an upper bound to the transmissibility of monkeypox; 2) we considered as imported cases all cases with a history of travel to Canary Islands; this assumption was considered as a baseline for the results in the main text; 3) we considered as imported cases all cases with a history of travel abroad; this is also an unrealistic hypothesis that can be considered as a lower bound to the transmissibility of monkeypox.
Cases for which there are no information for travel abroad are always assumed to be locally transmitted.
In Appendix Figure 3, we report estimates of the reproduction numbers for the 3 hypotheses (rows) as obtained by considering the mean and the lower and upper limits of the 95% CI of the generation time, namely 12.5 days, 7.5 days, and 17.3 days (columns). Appendix Table 5 reports the values of the average reproduction number during the first week of June (i.e., the last week for which the epidemic curve can be reasonably assumed to not suffer from diagnostic and reporting delays).
As a sensitivity analysis, we estimated the reproduction number under the assumption of exponential growth in the first week of June, computed from the formula above by forcing Rt to be constant over the first week of June. Appendix Table 6 shows the estimated value (mean and 95% CI) for all combinations of assumptions on imported cases and mean generation time. The values are in line with those of the main analysis, reported in Appendix