Strongly heterogeneous transmission of COVID-19 in mainland China: local and regional variation

Yuke Wang; Peter F.M. Teunis

Spreading patterns of COVID-19 at different spatial scales, from local (railway department and department store) to regional (cities within Guangdong Province) to nationwide (Provinces within China), appear similar: new cases arise from contacts with a reservoir, spreading to remote locations through travel from the origin outbreak region. There likely is some secondary spread locally, from cases infected from the reservoir, but local reproduction numbers are low, often insufficient to support sustained transmission. Knowledge of the serial interval, for symptomatic cases in the outbreak, is essential for analysis of the transmission probabilities [14] . Previous studies have estimated the distribution of serial intervals from a set of confirmed transmission pairs, where both the ancestor (who caused infection) and the descendant (who became infected) were known [19, 20] . As such information is mostly lacking [6] (and may be hard to obtain) in this COVID-19 outbreak, we have estimated the serial interval distribution from a curated network, using whatever contact information was available. Existing knowledge of contacts (and timing of those contacts) between cases was used to construct a matrix of prior probabilities, to restrict the transmission network to only those links that are possible. When all transmission links are known, the serial interval distribution can be easily estimated. However, at early stages of an outbreak, information on transmission links is usually incomplete. When a sufficiently large proportion of the transmission links is known, it is possible to estimate both the serial interval distribution, and the transmission probability matrix [14] . Starting from a plausible serial interval distribution, the transmission probability matrix V is updated until convergence; then V is frozen and the serial interval parameters are updated, again until obtaining a new optimum; then the serial interval distribution is frozen and the transmission probability matrix is updated again, and so on, until no further improvement can be found. The estimated serial interval distribution, Gamma(3·16,1·52), has a mean of 4·8 days and good spread out (i.e. large scale parameter) to long serial interval. The variation of serial interval could caused by highly varied incubation period [21] . Such a short serial interval, compared to SARS (mean: 8·4 days) [22] and MERS (mean: 6·8 days) [23], gives COVID-19 ability to spread more rapidly. The rapid spread of COVID-19 in South Korea (from 31 cases on 18 February to 2,022 cases on 28 February) and Italy (from 20 cases on 21 February to 650 cases on 28 February), shows how missed infectious subjects may cause rapid transmission within a very short period, due to the combination of a short serial interval and an occasionally high reproduction number [24] . As the incubation period seems to be highly variable, it may be possible that appearance of symptoms in any case precedes symptom onset in its ancestor. When that happens, the serial interval for symptom onset is negative. To check whether negative serial intervals would adversely affect analysis we used an alternative distribution, where the serial intervals were shifted leftward by a small amount. A shift of one or two days had no destructive effect on estimation of V , and the resulting estimates of the effective reproduction numbers did not change substantially.