Forecasting the cumulative number of COVID-19 deaths in China: a Boltzmann function-based modeling study

Gao, Yuanyuan; Zhang, Zuqin; Yao, Wei; Ying, Qi; Long, Cheng; Fu, Xinmiao

We first verified that the cumulative numbers of confirmed cases with respect to each region were all well fitted to the Boltzmann function (ie, all R 2 close to 0.999) (Fig. 1A) , consistent with our earlier report using the data from January 21 to February 14, 2020. 3 Assuming that the number of deaths is proportional to the number of confirmed cases for the outbreak under specific circumstances, we speculated that the cumulative number of COVID-19 deaths would also obey the Boltzmann function. In support of this speculation, the cumulative numbers of COVID-19 deaths in the aforementioned regions were all well fitted to the Boltzmann function (R 2 all being close to 0.999) (Figs. 1B, 1C and Table 1 ). The potential total numbers of deaths were estimated to be 3,200±40 in China, 108±1 in Hubei, 3,100±40 outside Hubei, 2,500±40 in Wuhan City, and 604±6 outside Wuhan (Table 1) . These results, in conjunction with our earlier observation that the cumulative numbers of confirmed cases of 2003 SARS in mainland China and worldwide were well fitted to the Boltzmann function, prompted us to analyze the cumulative numbers of 2003 SARS deaths in the same way. The cumulative numbers of 2003 SARS deaths in mainland China, Hong Kong, and worldwide were all well fitted to the Boltzmann function ( Fig. 1D ), strongly suggesting that the Boltzmann function is suitable to simulate the course of deaths associated with coronavirus-caused diseases.