A novel coronavirus began to spread from Wuhan in December 2019, and now infected cases are confirmed in almost every province in China; and in the past 10 days has flown to other Asian countries and across the Pacific as well, with over 7000 people infected globally so far. Hong Kong has imported 10 cases via its many ports directly bordering with the mainland. Though Hong Kong people are vigilant of the outbreak, the painful memory of SARS has created tremendous stress and fear. The question is: will Hong Kong repeat history and be in for another severe outbreak?
Here is my quick and crude analysis, based on limited data
Data
From 22/1 to 29/1, the number of confirmed cases in HK grew from 0 to 10.
23/1 +2 cases, total=2
24/1 +3 cases, total=5
26/1 +3 cases, total=8
29/1 +2 cases, total=10
Model
My model is based on the simple rationale that new cases are related to existing cases, both within HK and imported from Wuhan. To keep it simple, I assume the bigger Wuhan area being the entire mainland. So, for Hong Kong, it is sufficient to assume just Hong Kong-Wuhan(=Mainland) interaction. So, how fast our number grows depends on
1. our own number
2. Wuhan’s number
3. recovery rate (awareness, protection, etc)
Yes, this is essentially a simplified "SIR" model*, as the academics used to call it. So, I am just pulling out the following simple equation, assuming that the incubation period is 10 days, i.e., in any day, people who can infect you are actually 10 times more than the infected number because they do not have symptom in the first ~10 days after being infected. This is just
RateHK(t) = αHK * (10) * NHK + βHK * τHK * 10 * NW – γ * (NHK+NW)
where
RateHK(t) = rate of increase of infected cases, i.e., number of new cases per day;
NHK = number of infected cases in HK;
NW = number of infected cases in Wuhan (mainland);
α, β = infection rates;
γ = recovery rate;
τ = traffic factor (with this parameter, I can extend the model to other cities of the entire China).
Or equivalently, by redefining parameters for simplicity's sake (only for HK anyway), we have
RateHK(t) = ΑHK * NHK + ΒHK * NW – Γ * (NHK+NW)
Now, filling in the past data (limited though), the average rates in 22-23/1, 23-24/1 and 24-26/1 are
RateHK(ave) = 2 = ΑHK * 2 + ΒHK * 4000 – ΓHK * 0.05 * 4002
RateHK(ave) = 3 = ΑHK * 5 + ΒHK * 4500 – ΓHK * 0.1* 5005
RateHK(ave) = 1.5 = ΑHK * 8 + ΒHK * 6000 – ΓHK * 0.5 * 6008
The factor 0.05, 0.1 and 0.5 in the third term is to adjust the society’s awareness of self-protection that retards the transmission rate. At the beginning, awareness was very poor in the mainland, I would say 0.05 as the factor of awareness that reduces the recovery rate. Then, in later few days, people get better educated, say being improved to 0.1. Then, at the latest time, I assume that most are vigilant, hence 0.5. This factor is necessary unless we make alpha and beta time-varying to address the same effect.
Solving the equations from the data, we get ΑHK = 0.405, ΒHK = 0.0003782, and ΓHK = 0.0016.
Prediction
So, here we go (assuming full awareness of self-protection):
RateHK = 0.405 NHK + 0.0003782 NW – 0.0016 * 1.0 * (NHK+NW)
Just a bit of nasty arithmetics, averaging over next 30 days, NHK should be adjusted to NHK(now) + RateHK*15. So, the next 30 days, we have
RateHK = 0.405 (NHK(now)+RateHK*15) + 0.0003782 NW – 0.0016 * 1.0 * (NHK(now)+RateHK*15+NW)
Assume Wuhan’s outbreak continues in the next 4 weeks. Let’s speculate 3 scenarios, depending on the mainland situation and assuming that our borders remain opened (at least our CE had insisted it be so).
WORST: For extreme outbreak, let NW = 100000 average in Feb.
POOR: For severe outbreak, let NW = 50000 average in Feb
HOPEFUL: If outbreak in Wuhan (mainland) is under control, let NW = 10000 average in Feb.
PREDICTION of Rate_HK for next 30 days:
WORST: RateHK = 15 cases per day
POOR: RateHK = 7 cases per day
HOPEFUL: RateHK = 0 cases per day (as RateHK < 0)
Conclusion
I don't have enough data to establish a confidence level. Perhaps somewhere between HOPEFUL and POOR is the most likely event, as the mainland number continues to soar over 10,000!
I must also confess that I did not consider the contact network and individual behavior in the above analysis. So, not perfect though, still I would say they aren't completely unreasonable estimates.
30 January 2020
__________________*M. Small, P. Shi and C. K. Tse, "Plausible Models for Propagation of the SARS Virus," IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, vol. E87-A, no. 9, pp. 2379-2386, September 2004.M. Small, C. K. Tse, and D.M. Walker, "Super-spreaders and the rate of transmission of the SARS virus," Physica D, vol. 215, pp. 146-158, March 2006.
