The potential impact of expanding target age groups for polio immunization campaigns

BACKGROUND: Global efforts to eradicate wild polioviruses (WPVs) continue to face challenges due to uninterrupted endemic WPV transmission in three countries and importation-related outbreaks into previously polio-free countries. We explore the potential role of including older children and adults in supplemental immunization activities (SIAs) to more rapidly increase population immunity and prevent or stop transmission. METHODS: We use a differential equation-based dynamic poliovirus transmission model to analyze the epidemiological impact and vaccine resource implications of expanding target age groups in SIAs. We explore the use of older age groups in SIAs for three situations: alternative responses to the 2010 outbreak in Tajikistan, retrospective examination of elimination in two high-risk states in northern India, and prospective and retrospective strategies to accelerate elimination in endemic northwestern Nigeria. Our model recognizes the ability of individuals with waned mucosal immunity (i.e., immunity from a historical live poliovirus infection) to become re-infected and contribute to transmission to a limited extent. RESULTS: SIAs involving expanded age groups reduce overall caseloads, decrease transmission, and generally lead to a small reduction in the time to achieve WPV elimination. Analysis of preventive expanded age group SIAs in Tajikistan or prior to type-specific surges in incidence in high-risk areas of India and Nigeria showed the greatest potential benefits of expanded age groups. Analysis of expanded age group SIAs in outbreak situations or to accelerate the interruption of endemic transmission showed relatively less benefit, largely due to the circulation of WPV reaching individuals sooner or more effectively than the SIAs. The India and Nigeria results depend strongly on how well SIAs involving expanded age groups reach relatively isolated subpopulations that sustain clusters of susceptible children, which we assume play a key role in persistent endemic WPV transmission in these areas. CONCLUSIONS: This study suggests the need to carefully consider the epidemiological situation in the context of decisions to use expanded age group SIAs. Subpopulations of susceptible individuals may independently sustain transmission, which will reduce the overall benefits associated with using expanded age group SIAs to increase population immunity to a sufficiently high level to stop transmission and reduce the incidence of paralytic cases

Recipes for sparse LDA of horizontal data

Many important modern applications require analyzing data with more variables than observations, called for short horizontal. In such situation the classical Fisher’s linear discriminant analysis (LDA) does not possess solution because the within-group scatter matrix is singular. Moreover, the number of the variables is usually huge and the classical type of solutions (discriminant functions) are difficult to interpret as they involve all available variables. Nowadays, the aim is to develop fast and reliable algorithms for sparse LDA of horizontal data. The resulting discriminant functions depend on very few original variables, which facilitates their interpretation. The main theoretical and numerical challenge is how to cope with the singularity of the within-group scatter matrix. This work aims at classifying the existing approaches according to the way they tackle this singularity issue, and suggest new ones

Genetic Basis of Myocarditis: Myth or Reality?

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On the factorization of simplex basis matrices

In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the nontriangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior t