Density. The spectral densities are shown in Figure 2 which can be reasonably interpreted by comparatively examining the temporal distributions ( Figure 1 ). With regard to the data collected from The Hague and Berlin, the observations of which were made before the introduction of vaccinations, periodic epidemics (i.e., super-annual cycles) are apparent where the interepidemic period ranges from 3 to 5 years (see Figures  1(a) and 1(b) ). However, the annual cycle is not seen, and thus, the spectral densities do not show a clear seasonal pattern (Figures 2(a) and 2(b) ). On the contrary, the time series data in Zurich and Shanghai clearly revealed a peak at 12 months (Figures 2(c) and 2(f)). The entire Netherlands data covers a relatively short period of time compared to the other datasets (Figure 1(d) ) with unclear seasonal and periodic frequencies in the spectral diagram (Figure 2(d) ). Although a small peak is seen at 12 months for the data in the Northwest Frontier province in India (Figure 2(e) ), the density plot exhibits a multimodal pattern, reflecting an irregular temporal distribution (Figure 1(e) ). In the Bombay data, the annual cycle is most clearly highlighted in the temporal distribution (Figure 1(g) ), which is also reflected in the spectral density (Figure 2(g) ). Figure 3 plots estimates of the effective reproduction number as a function of calendar time. The vertical broken lines represent January in every year, while a horizontal dashed line is a reference value yielding R(t) = 1, that is, the threshold condition of an epidemic. R(t) tends to increase during the winter season for three early records (Figures 3(a), 3(b), and 3(c) ), but the annual cycles are not seen. However, the shortterm epidemic data for the entire Netherlands clearly shows that three peaks of R(t) coincide in every January with estimates above unity (Figure 3(d) ). A similar pattern is observed in Shanghai and Bombay (Figures 3(f) and 3(g) ). Figure 4 shows the spectral density plots of R(t) for the entire Netherlands and Northwest Frontier province in India. Although spectral densities of death and mortality (Figures 2(d) and 2(e)) did not exhibit a clear annual cycle, the obvious peak at 12 months is seen for both datasets in terms of R(t) (Figures 4(a) and 4(b) ). That is, seasonal patterns of smallpox transmission were reasonably shown with the use of R(t) even for the short-and long-term time series. Table 1 shows the output of univariate and multivariate models for explaining smallpox mortality in India using meteorological variables. In both models, rainfall was not significantly associated with smallpox mortality. However, significant negative association was found for humidity (adjusted MRR = 0.387 (95% confidence interval (CI): 0.311, 0.481), P < .01). Table 2 summarizes the relationship between the effective reproduction number and meteorological variables using a multiple linear regression model. On a whole, the model showed a weak predictive ability. However, humidity was again identified as an explanatory variable which significantly reduces the effective reproduction number (P < .01). No significant correlation was found between R(t) and rainfall.