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. 2018 Oct 17;13(10):e0205889.
doi: 10.1371/journal.pone.0205889. eCollection 2018.

Reconstructing the Transmission Dynamics of Rubella in Japan, 2012-2013

Free PMC article

Reconstructing the Transmission Dynamics of Rubella in Japan, 2012-2013

Masaya M Saito et al. PLoS One. .
Free PMC article


Background: Japan experienced a nationwide rubella epidemic from 2012 to 2013, mostly in urban prefectures with large population sizes. The present study aimed to capture the spatiotemporal patterns of rubella using a parsimonious metapopulation epidemic model and examine the potential usefulness of spatial vaccination.

Methodology/principal findings: A metapopulation epidemic model in discrete time and space was devised and applied to rubella notification data from 2012 to 2013. Employing a piecewise constant model for the linear growth rate in six different time periods, and using the particle Markov chain Monte Carlo method, the effective reproduction numbers were estimated at 1.37 (95% CrI: 1.12, 1.77) and 1.37 (95% CrI: 1.24, 1.48) in Tokyo and Osaka groups, respectively, during the growing phase of the epidemic in 2013. The rubella epidemic in 2012 involved substantial uncertainties in its parameter estimates and forecasts. We examined multiple scenarios of spatial vaccination with coverages of 1%, 3% and 5% for all of Japan to be distributed in different combinations of prefectures. Scenarios indicated that vaccinating the top six populous urban prefectures (i.e., Tokyo, Kanagawa, Osaka, Aichi, Saitama and Chiba) could potentially be more effective than random allocation. However, greater uncertainty was introduced by stochasticity and initial conditions such as the number of infectious individuals and the fraction of susceptibles.

Conclusions: While the forecast in 2012 was accompanied by broad uncertainties, a narrower uncertainty bound of parameters and reliable forecast were achieved during the greater rubella epidemic in 2013. By better capturing the underlying epidemic dynamics, spatial vaccination could substantially outperform the random vaccination.

Conflict of interest statement

The authors declare that co-author H. Nishiura is a PLOS ONE Editorial Board member. This does not alter the authors’ adherence to all the PLOS ONE policies on sharing data and materials. Apart from this membership, the authors declare that they have no conflicts of interest.


Fig 1
Fig 1. Epidemic curve of the rubella epidemic from 2012 to 2013, Japan.
Top: Weekly number of notified cases in Kanto (Tokyo and adjacent prefectures), Kansai (Osaka and adjacent prefectures) and the rest of Japan. Middle and bottom: The number of notified cases in Tokyo (middle) and Osaka (bottom) in log-scale. Epidemic periods are represented by gray-shaded areas, which were visually determined by linear/eyeball extrapolation of the trend, i.e., the epidemic period is switched when the increasing or decreasing trend is swapped.
Fig 2
Fig 2. Posterior distributions of the effective reproduction number.
Marginal posterior distributions of the effective reproduction numbers are shown for different annealing temperatures (i.e., 16, 32 and 64), as obtained from 40,000 chains. Group 1 represents Tokyo and adjacent prefectures, while group 2 represents Osaka and adjacent prefectures. Tokyo has six panels while Osaka has only five because the epidemic period in Osaka was less complex than Tokyo (see Fig 1). The vertical black line shows the posterior mean value, while the vertical dashed line shows the posterior map (i.e., maximum a posteriori) value, which yields the greatest likelihood value.
Fig 3
Fig 3. Effective reproduction number of the rubella epidemic from 2012 to 2013, Japan.
The posterior mean (continuous line) and 95% credible intervals (CrI; dashed lines) are shown. Black bars represent group 1, i.e., Tokyo and adjacent prefectures, while white bars represent group 2, i.e., Osaka and adjacent prefectures. Monte Carlo particles yielded by the chain with annealing temperature 32 are used for obtaining these estimates. Day 0 is 2 January 2012.
Fig 4
Fig 4. Forecasting rubella epidemics in 2012 and 2013, Japan.
Forecasts with 95% prediction intervals for six prefectures are shown. Six prefectures with different population size (each estimate on the upper right corner) are chosen and displayed. For the 2012 forecasting, we repeated the filtering process up to 112th day (when an exponential growth in the first year begins) and repeated the prediction process up to the end of the epidemic. Forecasted weekly notifications are shown in log-scale. Mean and 95%CrIs in filtering process are displayed by solid curves and gray-shaded areas, respectively. For the 2013 forecasting, the filtering process was continued up to 308th day on which an exponential growth in the second year began.
Fig 5
Fig 5. Comparison of the forecast error between metapopulation and homogeneous models.
The horizontal axis measures the date on which forecasting was made. The vertical axis measures the root mean square error (RMSE), representing error value. For the homogeneous model, the SIR model without spatial structure was fitted to the dataset for all of Japan. Subsequently, infected individuals were proportionately allocated to each prefecture by population size, so that the prefecture-specific forecast can be compared. Metapopulation was labeled as “meta-population,” while the stochastic SIR model was labeled as “aggregated.” Day 0 is 2 January 2012. Days are counted onward; thus, year 2013 starts on Day 365.
Fig 6
Fig 6. Predicted cumulative incidence by different spatial vaccination scenarios.
Cumulative incidence is measured on the vertical axis. The spatial vaccination scenario assumes that we have enough vaccines to increases the immune fraction of the entire Japan by 1% (left), 3% (middle) and 5% (right), respectively, following each policy. Vaccination was assumed to take place in advance of the 2012 epidemic. The horizontal axis represents the number of prefectures to be covered by vaccination. For instance, the value of 4 indicates that vaccination is prioritized only for Tokyo, Kanagawa, Osaka and Aichi prefectures, i.e., the top four populous prefectures. The value of 47 indicates that vaccines are equally distributed to all prefectures. Median trajectory is represented by a continuous curve. Outer most curves are the 95% credible intervals. Other points are drawn using dotted lines for every 10th percentile point (i.e., 10th, 20th,…, 90th).

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Grant support

HN received funding from the Japan Agency for Medical Research and Development (AMED; grant numbers JP18fk0108050 and JP18fk0108066), Japanese Society for the Promotion of Science (JSPS) KAKENHI (grant numbers 16KT0130, 16K15356 and 17H04701), The Telecommunications Advancement Foundation and Inamori Foundation. All authors were financially supported by Japan Science and Technology Agency (JST) CREST program (JPMJCR1413). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.