The estimates for effective reproduction number R obtained from the confirmed case and hospitalization data are in good agreement, with R in the range of 1.04-1.27 for the first summer wave during July-September, and 1.01-1.05 for the second wave in fall/winter, using the generation time estimated by  for the spring outbreak in Mexico. Serological evidence has indicated that approximately one in every ten persons was infected with the 2009 pH1N1 virus in central Taiwan by April-June [1, 27]; hence the estimates using data after July does not yield, and can reasonably be expected to be lower than, the more commonly known basic reproduction number R0.
A recent modeling study  of the 2009 pH1N1 epidemic by geographic region in Mexico reveals a three-wave pandemic, with an initial wave in April-May (Mexico City area), a second wave in June-July (southeastern states), and a geographically widespread third wave in August-December. The estimates for the regional reproduction numbers R were 1.8-2.1, 1.6-1.9, and 1.2-1.3 for the spring, summer, and fall waves, respectively. The second and third waves in Mexico occurred, respectively, one month earlier than the summer (July-early September) and fall/winter (late September-March 2010) waves in Taiwan under study here and exhibit similar decreasing trend, although with higher R.
Transmissibility of the fist pH1N1 wave in Taiwan during the summer in July-September, as measured by R, was lower than that of the earlier spring outbreak in North America [20, 26, 29, 30] and Europe , most likely, at least in part, due to decreased social contacts among the population triggered by public awareness of the earlier, well-publicized outbreaks in Mexico and North America as well as the subsequent preemptive government campaign to reduce transmissions. It was also lower than that of the winter outbreak in the Southern Hemisphere around the same time [19, 32, 33], perhaps attributable to the fact that it was the winter influenza season in the Southern Hemisphere. Moreover, It is lower than the final size estimate of R0 (1.87; 95% CI: 1.68-2.06) obtained from serological study of a cohort household population in central Taiwan during the same period of time . However, we note that this disparity is reasonable since the serologic data used for this estimate accounts for the asymptomatic cases among the cohort group. The decreased transmissibility (smaller R) during fall/winter can be reasonably attributed to increased community-wide immunity from the first wave, and perhaps to the 325 class suspension policy initiated in early September before the start of the fall/winter wave.
Significantly higher estimate of R (focused on schoolchildren) in the range of 2.0-2.6 was found for the initial pandemic wave in Japan . Using updated epidemic data and an age-structured model, the same authors also estimated R for the subsequent community-wide wave in Japan in early summer to be much lower (1.21-1.35) , although different population and modeling methodology also may have played a role in the decrease in R in subsequent waves. Similar decreases in estimates of reproduction number of 2009 H1N1 when more than one pandemic wave had occurred have been reported in many countries, including Mexico , Argentina and Brazil , Canada , and Japan [34, 35]. Furthermore, these studies show that it is not uncommon for multi-wave outbreaks to be more transmissible in a first wave but less widespread with a smaller number of infections (or perhaps limited to a small subpopulation as was in the case of pH1N1 in Japan), when compared to subsequent waves. Moreover, the second wave in Taiwan started shortly after the school opened in September, when additional infections occurring in school settings (as demonstrated by substantial number of class suspensions) contributed to a large number of cases, but perhaps with relatively less per contact transmissibility when compared to household contacts, as it has been reported that sitting next to a case or being the playmate of a case did not significantly increase the risk of H1N1 infection .
The estimates for R using laboratory-confirmed case data by sample receiving weeks are slightly lower than those obtained by using confirmed hospitalization data. Although both the confirmed case and hospitalization datasets identify week 39 as the cutoff week for the two waves, the estimates of turning points for each wave differ by about one week when using the two datasets. Since only the more severe confirmed cases were hospitalized, the individuals in the resulting hospitalization time series is a selected subset of those in the confirmed case time series. Subsequently, the temporal trends of the two time series might not be closely comparable. However, the cumulative curves in Figures 2, 3, 4, 5 indicate some similarity in the temporal trends of the cumulative data, mainly in the form of the turning points. The reproduction numbers of the two datasets, on the other hand, are indeed comparable since they mostly are generated from the initial growth rates and hence less affected by any selection bias.
The confirmed case data is generated by sampling week, which could be different from the week of symptom onset and hence pose a potential source of some bias in data. However, samples were typically taken when the physicians diagnosed and reported H1N1 cases. We refer to 2003 SARS outbreak in Taiwan, when it was estimated that the onset-to-diagnosis interval is 1.20 days for previously quarantined persons and 2.89 days for non-quarantined persons . Given the similarity in symptoms of SARS and influenza as well as the heightened public awareness due to the world-wide alarm over the seriousness of the pH1N1 pandemic by September, it is more than likely that the time delay from symptom onset to diagnosis (and sample collection) of pH1N1 cases in Taiwan would be no more, if not less, than that of 2003 SARS. Moreover, one would expect that the lesson of SARS and the subsequent efforts by the government to educate has taught the general public in Taiwan to avoid delays in seeking medical care. Subsequently, this delay of one or two days in the weekly data can be expected to be most likely not significant. The use of hospitalization data is mainly for the purpose of estimation of reproduction number and comparison with the resulting estimates using the confirmed case data, which is not affected by this delay that might be present in both data.
Estimates of R obtained by using other (larger) estimated generation time in literature result in larger values for R, but generally are well within the ranges of the other studies (see, e.g., [19, 20, 26, 29–32] and Table 2) and hence is omitted for brevity. Note also that the formula for R used here yields an upper bound over all possible distributions for T given the growth rate r, and hence might result in an overestimate of its true value.
In Taiwan, the fall session for kindergarten to high school started on August 31, while the universities started the fall semester two weeks later, around mid-September. Our analysis using the weekly confirmed case and confirmed hospitalization data shows that the initial summer wave of pH1N1 epidemic in Taiwan had peaked by e-week 36-37 (8/30-9/12), around the time schools from kindergarten to grade 12 reopened on August 31. However, a second fall/winter wave of cases started to emerge near the end of September around e-week 39 (9/27-10/3), approximately 4 weeks after the schools reopened, which did not reach its peak until mid-November (e-week 46-47 or 11/8-11/21) and lasted until the turn of the year. It is interesting to note that the state-specific fall pandemic waves in Mexico began 2-5 weeks after school reopened , which is consistent with our results on the start of the fall wave in Taiwan. Note that both turning points of the two waves in Taiwan fell on neighboring week using either the lab-confirmed case or hospitalization data. This is reasonable since the hospitalization of confirmed cases and the time that the samples were received by laboratories are closely related, although not necessarily in any particular order.
The class suspension data started on September 9 near the end of the first wave when the earliest class suspension occurred, according to our 2-wave fitting in Tables 1 and 2, hence only one wave was modeled via the Richards model (Table 3). Moreover, November 19 (95% CI: November 18-20) was determined to be the turning point for the daily class suspension data, while November 17 (95% CI: November 16-18) is the turning point for the daily number of schools with class suspended. Both days fall on e-week 47, which coincides with the week where the turning point had occurred as pinpointed by using the confirmed case data and one week after the turning point obtained by using the hospitalization data. It is reasonable to expect the class suspension to take place following the occurrence of case reporting and hospitalization. Moreover, the use of daily data allows a more precise estimation of the turning point.
Also of interest is the possible impact of major intervention measures implemented by the Taiwan government during this time period, which including the aforementioned "325 class suspension" policy and the mass immunization program. The daily number of class suspensions started to increase in early September and continued until late November after the implementation of mass immunization campaign (Figure 1). In particular, the 325 policy, which was designed to minimize the potential social impact of full-scale school closings in the event of a major influenza outbreak in the community; deserve special attention to ascertain its actual effectiveness. In fact, the lower estimates of R for the second wave and for the school closings data might indeed be attributable to the possible effects of school closings after September. However, more detailed class suspension data as well as age-specific epidemic data is needed to further quantify the actual impact or effectiveness of this very unique approach of partial school closure and localized class suspensions on the infections in the school and in the community in a qualitative modeling analysis (see, e.g., [12, 13, 38]).