Doubling time tells how effective Covid-19 prevention works

Byung Mook Weon

The Cobid-19 has been spreading rapidly in many countries since it was first discovered in December 2019 [1, 2] . The total confirmed cases of Covid-19 for 12 countries are shown in Fig. 1A , retrieved from the Johns Hopkins University [3] . Each country has more than 4,500 cases as of March 23. The initial growths of the total cases for 12 countries exhibit the exponential growth dynamics, as in Fig. 1B . In general, the exponential growth of the total cases is represented by N = N 0 exp(γt) where N 0 and N are the total cases at time t 0 and t, respectively, and γ is the growth rate. By definition, N = 2N 0 needs the doubling time (α) that is expressed as α = ln(2)/γ through ln(N/N 0 ) = ln(2) = γt. If the growth rate evolves with time, depending on the effective prevention strategies, then the doubling time changes with time. Thus, the time-dependent growth rate γ(t) causes the time-dependent doubling time α(t), defined as α(t) = t ln(2)/ ln(N/N 0 ) through γ(t) = ln(N/N 0 )/t. The doubling time for 12 countries (Fig. 1C ) was analyzed (Appendix 1). For China, the doubling time has declined until January 28 and then increased linearly since early February, due to the Wuhan containment since January 23. In South Korea, the doubling time has increased linearly without any initial decline. Since the early periods, South Korea has applied effective strategies, such as mass testing and patient tracking, to both symptomatic and asymptomatic patients [4] . The steady increases in the doubling times eventually lead to the flattened total case curves for China and South Korea [2] . In other countries, the increase of the doubling time was not sufficient to flatten the total case curves. How effective preventive measures work [5] can be evaluated by tracking the doubling time. As demonstrated here, the time-dependent doubling time is real and informative.