The Smooth Ideal

We give a classical proof of the generalization of the characterization of smoothness to quotients of Polish spaces by Borel equivalence relations. As an application, we describe the extent to which any given Borel equivalence relation on a Polish space is encoded by the corresponding σ-ideal generated by the family of Borel sets on which it is smooth.</p

Additional file 3 of Efficacy of a bivalent killed whole-cell cholera vaccine over five years: a re-analysis of a cluster-randomized trial

Supplementary Text (Model equations). (PDF 45.5 kb

Additional file 2 of Efficacy of a bivalent killed whole-cell cholera vaccine over five years: a re-analysis of a cluster-randomized trial

Figure S1. (PDF 27.4 kb

Estimated response times to mount a mass oral cholera vaccination campaign, using a single-dose vaccine.

<p>Estimated response times to mount a mass oral cholera vaccination campaign, using a single-dose vaccine.</p

Population, number of culture-positive cholera cases each year, and incidence (per 1000 population per year) in study sites in three countries.

*<p>Two census data sets, collected 12 months apart were available. The mean of the two censuses is reported.</p>**<p>Surveillance did not include pregnant women and children <2 years of age.</p>***<p>Rates were corrected for direct protection from cholera vaccination.</p

The number of cases that would have been prevented during the initial outbreak and in the years following vaccination.

<p>The total number of cases which would have been prevented during the first outbreak and in the years following mass vaccination using the currently licensed two-dose oral cholera vaccine with 50% vaccine coverage, and 85% PE in first 6 months, 60% PE from 6 to 18 months, and 20% for the following 3 years, at variable response times.</p

Estimated reduction in cholera cases in Zanzibar.*

<p>3a: During the 2006–07 outbreak in Unguja following a <u>rapid</u> mass oral cholera vaccine campaign with 50% coverage. 3b: During the 2006–07 outbreak in Unguja following a <u>delayed</u> mass oral cholera vaccine campaign with 50% coverage. 3c: During the 2006–07 outbreak in Unguja following a mass oral cholera vaccine campaign with <u>maximum delay</u> and 50% coverage. 3d: During the 2006–07 outbreak in Pemba following a <u>rapid</u> mass oral cholera vaccine campaign with 50% coverage. 3e: During the 2006–07 outbreak in Pemba following a <u>delayed</u> mass oral cholera vaccine campaign with 50% coverage. 3f: During the 2006–07 outbreak in Pemba following a mass oral cholera vaccine campaign with <u>maximum delay</u> and 50% coverage. *See <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0000952#pntd-0000952-t002" target="_blank">Table 2</a> for the time point symbolized by each arrow. Figures show the epicurve of the outbreak and the hypothetical number of cases prevented at response time.</p

Estimated reduction in cholera cases in Kolkata.*

<p>2b: During the 2003 outbreak following a <u>delayed</u> mass oral cholera vaccine campaign with 50% coverage. 2a: During the 2003 outbreak following a <u>rapid</u> mass oral cholera vaccine campaign with 50% coverage. 2c: During the 2003 outbreak following a mass oral cholera vaccine campaign with <u>maximum delay</u> and 50% coverage. 2d: During the <u>2004</u> outbreak following a <u>rapid</u> mass oral cholera vaccine campaign with 50% coverage. 2e: During the <u>2004</u> outbreak following a <u>delayed</u> mass oral cholera vaccine campaign with 50% coverage. 2f: During the <u>2004</u> outbreak following a mass oral cholera vaccine campaign with <u>maximum delay</u> and 50% coverage. *See <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0000952#pntd-0000952-t002" target="_blank">Table 2</a> for the time point symbolized by each arrow. Figures show the epicurve of the outbreak and the hypothetical number of cases prevented at response time.</p

Cases that would have been prevented by mass oral vaccination oral cholera vaccine in three endemic sites.

<p>Mass vaccination is presumed to be using the currently licensed two-dose oral cholera vaccine at varying response times and vaccine coverage.</p

Estimated reduction in cholera cases during the Zimbabwe 2008–09 outbreak.*

<p>1a: Following a <u>rapid</u> mass oral cholera vaccine campaign with 50% coverage. 1b: Following a <u>delayed</u> mass oral cholera vaccine campaign with 50% coverage. 1c: Following a mass oral cholera vaccine campaign with <u>maximum delay</u> and 50% coverage. *See <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0000952#pntd-0000952-t002" target="_blank">Table 2</a> for the time point symbolized by each arrow. Figures show the epicurve of the outbreak and the hypothetical number of cases prevented at response time.</p