Quantitative evaluation on control measures for an epidemic: A case study of COVID-19

ABSTRACT

The spread of an epidemic should be a phenomenon governed by the natural growth law More infected beget more infections. This basic rule would be useful especially when an outbreak is caused by a novel virus with its basic characteristics full of unknowns so much that there would be too many uncertainties that would be impossible for anyone to run the traditional epidemiological model meaningfully. The natural growth law does not depend on the detailed characteristics of the virus. When it is employed, a transmission rate can be defined and determined directly from clinical field data, which can change following the course of the epidemic development. Such a data driven natural growth model has been developed to track the development for any epidemic. It can yield useful information on the propagation pattern of the epidemic dynamically. The transmission rate so determined is sensitive enough not only to track the course of the epidemic but also to reveal the effects of control measures quantitatively. Importantly, it offers the potential to make predictions for epidemic management. In December 2019, a severe epidemic, the novel coronavirus epidemic, now designated as the COVID-19, broke out in Wuhan, China. It spread quickly in and around Wuhan. To complicate the situation, the outbreak initial period also coincided with the travel peak related with the Spring Festival. To prevent its spreading, Chinese government has instituted strict quarantine by lockdown the City and the surrounding Hubei Province. This drastic quarantine measure seemed to have slowed down the spread of the COVID-19 markedly. However, to evaluate the control effects quantitatively remains a challenge. In this paper, we propose to quantify the effectiveness of the quarantine using the natural growth model. Based on the model, we first estimated the transmission rates of the COVID-19 for different typical periods as follows In December 2019, the transmission rate is about 0.26;in the late January 2020, it is between 0.40 and 0.46. Therefore, if the strict quarantine measures had not been instituted for the epidemic at all, 16.98 million to 76.11 million people would have been infected under the transmission rate between 0.40 and 0.46, as of February 18, 2020, according to the model. Even for a very low transmission rate as 0.26, there would have been 513 thousand infected as of February 18, 2020, far greater than the actual data of some 58 thousand reported by the Chinese National Health Commission. The model can also be used to estimate the consequence of putting off the control measures. We conducted a hypothetical study as follows. We divided the development of the epidemic into three stages Before January 24, 2020, the infection grew as the actual situation does;from January 25, 2020 to the day before the supposed date of the start of the control measures, the infection grew with a transmission rate of 0.45;from the supposed date of the start of the control measure onwards, the infection took the actual transmission rate starting from January 25 on. Our model results indicate that the more days delayed for the quarantine measures, the faster increase of the infections. If the strict control measures were pushed back by one day (or 7 days), there would be 27 (or 785) thousand more infected cases than the reported as of February 18, 2020 in the whole China, in which 12 (or 493) thousand are in the Hubei Province. The above estimation is quite conservative. Less infected is easier to control;therefore, putting the measure control off we will have even more infected than estimated that would made the epidemic even harder to contain.