I give a web tool to compute the estimated total number of cases, by allowing you to interactively adjust the predefined values.
Another tryout (In Chinese) using Idyll+vega-lite can be seen here.
Drag on the numbers to change the value.
Suppose we have confirmed cases abroad Number of cases confirmed with severity (that need hospitalisation).
Let us further assume that everyday, passengers go abroad from the Wuhan Airport.
The population The catchment population of Wuhan Airport area
of Wuhan City that live near by the Wuhan Airport is million
and the duration window of 2019-nCoV is days (including incubation and the develop of symptoms until detection).
Then the estimated total number of cases in Wuhan is .
Imai et al. (2020Imai, Natsuko, Ilaria Dorigatti, Anne Cori, Steven Riley, and Neil M. Ferguson. 2020. “Estimating the potential total number of novel Coronavirus cases in Wuhan City, China.” Imperial College London .), a research group from Imperial College London, made a simple estimation of the total number of the novel Coronavirus (2019-nCoV) cases stemmed recently in Wuhan City, China. The method of estimation is in general valid and sound1 I will say it is too naive and simple. Yet it does have certain degree of concerns:
Here I provided an interactive estimation, where you can manipulate the values of assumptions and see how this will change the final result accordingly2 For example, if there are more abroad cases identified.
Basically, the estimated total number is computed by maximum likelihood estimation(MLE). But since it is under a bionomial assumption, in fact it is just computed in a very straight forward manner.
num_intl_case = 3 # Exported number of confirmed cases
num_intl_passenger = 3301 # Daily international passengers travelling out of Wuhan International airport
catchment_in_million = 19 # (in million) Effective catchment population of Wuhan airport
catchment = catchment_in_million * 10^6
detection_window = 10 # (in days) Detection window
p_intl_daily = num_intl_passenger / catchment # daily prob of international travel
p = p_intl_daily * detection_window # the probability any one case will be detected overseas
num_case = num_intl_case / p # the final result, total number of cases,
print(num_case)## [1] 1726.749 num_case = as.integer(num_case)
print(num_case)## [1] 1726There are, in fact, many other assumptions underlying the performed esimation.How would the number change, if the assumptions change?
The detection window is 10 daysThe longer the detection window, the smaller the estimated total number of cases, including incubation and the time for developing symptoms into final detection. The incubation period of 2019-nCoV is not known and has been approximated withthe estimates obtained for MERS-CoV and SARS.
the population of Human is also approximated. The longer the detection window, the smaller the estimated total number of cases
We assume that international travel is independent of the risk of exposure to 2019nCoV or of infection status.
I will not think it is a decently advanced modelling, this entirety of thing to me is too 20-century basic. But I nonetheless understand the difficulty here, you just do not have the auxiliary information to go sophisticated: you only got these simple data, then you only got to do it simply.