Records. Seven temporal distributions of smallpox at different times and locations were extracted from historical literature. This literature review was based on references collected by tracking all the references given in the relevant publications and repeating this task until we could find no further references; the details are given elsewhere [37, 38] . Figure 1 shows the time series data by location with a monthly reporting interval. Chronologically, epidemic records for The Hague (1755-1773), Berlin (1758-1774), Zurich (1870-1887), the entire Netherlands (1870-1873), Northwest Frontier province in India (1890-1921), Shanghai (1900) (1901) (1902) (1903) (1904) (1905) (1906) (1907) (1908) (1909) (1910) (1911) (1912) (1913) , and Bombay (1902) (1903) (1904) (1905) (1906) (1907) provide monthly data of smallpox with time and were used for further analysis [17, [39] [40] [41] [42] [43] [44] [45] . The first two records contain data before the introduction of vaccination. Except for Zurich, which documents the monthly number of cases, the remaining datasets record only monthly deaths. Death data are given as the absolute number of deaths, except where indicated. With regard to the magnitude of the epidemics, the annual averages of the disaster size were 10.1 deaths (The Hague), 32.9 deaths (Berlin), 9.9 cases (Zurich), 428.6 deaths (the entire Netherlands), 5.28 deaths per 100 000 (Northwest Frontier province in India), 21.5 deaths (Shanghai), and 2.45 deaths per 100 000 (Bombay). By examining another historical record of the smallpox epidemic in Tokyo, it was found that the mean (and the standard deviation) and the median (25-75% quartile) time from onset to death were 29.1 (13.8) and 26.0 (19.0-37.0) days, respectively [46] . Thus, it is reasonable to assume that the relative frequency of death with time represents that of onset accompanied by approximately a 1 month delay. Moreover, the infection may have happened approximately half a month before the onset [9] . Meteorological variables with time were given only in Rogers's observations [17] , which contained the monthly rainfall (inch) and the absolute humidity.