BACKGROUND: To improve understanding of influenza and rurality, we investigated differences in influenza testing and anti-viral treatment rates between micropolitan (muSAs) and metropolitan statistical areas (MSAs) using national medical claims data over multiple influenza seasons. METHODS: Using billing data from the Centers for Medicare and Medicaid Services for those aged 65 years and older, we estimated weekly rates of ordered rapid influenza diagnostic tests (RIDT) and antivirals (AV) among Medicare enrollees by core-based statistical areas (CBSAs) during 2010-2016. We used Negative Binomial generalized mixed models to estimate adjusted rate ratios (aRR) between MSAs and muSAs, adjusting for clustering by CBSA plus explanatory variables. We ran models for all weeks and only high influenza activity weeks. RESULTS: For all weeks, the unadjusted rate of RIDTs was 1.97 per 10,000 people in MSAs compared with 2.69 in muSAs (Rate ratio (RR) = 0.73, 95% Confidence Interval (CI): 0.73-0.74) and of AVs was 1.85 in MSAs compared with 1.40 in muSAs (RR = 1.32, CI: 1.31-1.32). From the multivariate model, aRR for RIDTs was 0.82 (0.73-0.94) and for AVs was 1.12 (1.04-1.22) in MSAs versus muSAs. For high influenza activity weeks, aRR for RIDTs was 0.82 (0.73-0.92) and for AVs was 1.15 (1.06-1.24). All models found influenza testing rates higher in muSAs and treatment rates higher in MSAs. CONCLUSIONS: Our study found lower testing and higher treatment in U.S. metropolitan versus micropolitan areas from 2010 to 2016 for those aged 65 years and older in our population. Identifying differences in influenza rates by rurality may improve public health response. Further research into the relationship of rurality and health disparities is needed.

A signed graph is a pair (G,Σ), where G=(V,E) is a graph (in which parallel edges are permitted, but loops are not) with V={1,…,n} and Σ⊆E. The edges in Σ are called odd and the other edges of E even. If there are parallel edges, then only two edges in each parallel class are permitted, one of which is even and one of which is odd. By S(G,Σ) we denote the set of all symmetric n×n matrices A=[a_i,j] with a_i,j<0 if i and j are connected by an even edge, a_i,j>0 if i and j are connected by an odd edge, a_i,j∈R if i and j are connected by both an even and an odd edge, a_i,j=0 if i≠j and i and j are non-adjacent, and a_i,i∈R for all vertices i. The maximum nullity M(G,Σ) of a signed graph (G,Σ) is the maximum nullity attained by any A∈S(G,Σ). Arav et al. gave a combinatorial characterization of 2-connected signed graphs (G,Σ) with M(G,Σ)=2. In this paper, we give a complete combinatorial characterization of the signed graphs (G,Σ) with M(G,Σ)=2.

A hollow matrix described by a graph G is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in G. For a given graph G, the determination of all possible spectra of matrices associated with G is the hollow inverse eigenvalue problem for G. Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs.