One-dimensional hyperbolic tangent performance.

<p>For the one-dimensional hyperbolic tangent test function (18), the Separatrix Algorithm outperforms Latin hypercube sampling and traditional BDOE on a likelihood-based performance metric (19).</p

Parameters values.

<p>Separatrix parameter values used in the three example presented in this paper.</p

Two-dimensional hyperbolic tangent performance.

<p>The Separatrix Algorithm again outperforms Latin hypercube sampling on the mean log likelihood metric, which was evaluated at points spaced evenly in arc-length along the separatrix.</p

The Separatrix Algorithm addresses two main sub-problems.

<p>The first is to use observed binary outcomes (top) to estimate the probability of success (bottom), and the second is to choose new points to sample. This is done so as to identify a particular isocline, called the separatrix, as illustrated by the dashed gray line.</p

Malaria model separatrix results.

<p>The separatrix (A), variance (B), and samples with density (C) after simulating the malaria model times.</p

One-dimensional hyperbolic tangent analysis.

<p>(A) Shown are the true success probability function (dashed line), LHS samples (full and empty circles), the inferred distribution (hypercolor), and the most likely value (black line). The vertical magenta line is at the separatrix corresponding to an interest level of . (B) The probability density after observing samples using the Separatrix Algorithm. Note that the estimate is tight near the separatrix. (C) The inner workings of the igBDOE algorithm. First, test and sample points are loaded from the previous iteration in which they were sampled from the variance of the interest distribution, solid black (left axis), which in turn is computed from the interest distribution: is in blue-dash and is in red dash-dot. The expected KL divergence is plotted for each of the candidate sample points (green circles, right axis). The best of these candidates, indicated by red crosses, will be selected. (D) The final density estimate shows that the igBDOE algorithm was placing samples in and around the separatrix. Ticks on the x-axis represent samples.</p

Quantifying the Impact of Expanded Age Group Campaigns for Polio Eradication

<div><p>A priority of the Global Polio Eradication Initiative (GPEI) 2013–2018 strategic plan is to evaluate the potential impact on polio eradication resulting from expanding one or more Supplementary Immunization Activities (SIAs) to children beyond age five-years in polio endemic countries. It has been hypothesized that such expanded age group (EAG) campaigns could accelerate polio eradication by eliminating immunity gaps in older children that may have resulted from past periods of low vaccination coverage. Using an individual-based mathematical model, we quantified the impact of EAG campaigns in terms of probability of elimination, reduction in polio transmission and age stratified immunity levels. The model was specifically calibrated to seroprevalence data from a polio-endemic region: Zaria, Nigeria. We compared the impact of EAG campaigns, which depend only on age, to more targeted interventions which focus on reaching missed populations. We found that EAG campaigns would not significantly improve prospects for polio eradication; the probability of elimination increased by 8% (from 24% at baseline to 32%) when expanding three annual SIAs to 5–14 year old children and by 18% when expanding all six annual SIAs. In contrast, expanding only two of the annual SIAs to target hard-to-reach populations at modest vaccination coverage—representing less than one tenth of additional vaccinations required for the six SIA EAG scenario—increased the probability of elimination by 55%. Implementation of EAG campaigns in polio endemic regions would not improve prospects for eradication. In endemic areas, vaccination campaigns which do not target missed populations will not benefit polio eradication efforts.</p></div

Model calibration and the effect of both expanding age groups and targeting in SIA campaigns.

<p>(A) Likelihood of polio infectiousness parameters: relative probability of reproducing the observed seroprevalence data from a sample of the model results conducted in the same manner (number of samples by age) as in the original Zaria serosurvey. Each tick mark represents a two-fold change in likelihood. (<b>B</b>) The effect of expanded age group SIA campaigns on elimination: distributions of mean WPV1 prevalence for baseline (calibration), EAG campaigns, and a campaign targeting hard-to-reach groups.</p

Effect of expanding age groups in SIA campaigns on mucosal immunity.

<p>(<b>A</b>) Mucosal antibody titer distribution before and after expanded age group campaigns in the overall population (5–9 years) and (<b>B</b>) the unvaccinated group (5–9 years) only. log₂(mucosal antibody titer)<3 represents high susceptibility to infection.</p

Distribution of cases by age (in years) during previous polio outbreaks for endemic and previously polio-free countries.

<p>The number of confirmed type 1 cases, mean age of infection, standard deviation of infection age, proportion of cases under five years old, and duration of case data used are in the table to right. High endemic countries are those that have sustained continuous transmission: India (IND), Afghanistan (AFG), Pakistan (PAK), and Nigeria (NGA). Low endemic areas are those that are exposed periodically to virus due to regular importations: Chad (TCD) and Niger (NER). Importation countries are those that have not reported WPV transmission since at least 2000: Democratic Republic of Congo (COD), Namibia (NAM), Tajikistan (TJK), and Republic of Congo (COG). Information compiled from multiple AFP databases maintained by WHO HQ, regional and country offices.</p