Background Rocky Mountain spotted fever (RMSF) is a disease that now causes significant morbidity and mortality on several American Indian reservations in Arizona. Although the disease is treatable, reported RMSF case fatality rates from this region are high (7%) compared to the rest of the nation (<1%), suggesting a need to identify clinical points for intervention. Methods The first 205 cases from this region were reviewed and fatal RMSF cases were compared to nonfatal cases to determine clinical risk factors for fatal outcome. Results Doxycycline was initiated significantly later in fatal cases (median, day 7) than nonfatal cases (median, day 3), although both groups of case patients presented for care early (median, day 2). Multiple factors increased the risk of doxycycline delay and fatal outcome, such as early symptoms of nausea and diarrhea, history of alcoholism or chronic lung disease, and abnormal laboratory results such as elevated liver aminotransferases. Rash, history of tick bite, thrombocytopenia, and hyponatremia were often absent at initial presentation. Conclusions Earlier treatment with doxycycline can decrease morbidity and mortality from RMSF in this region. Recognition of risk factors associated with doxycycline delay and fatal outcome, such as early gastrointestinal symptoms and a history of alcoholism or chronic lung disease, may be useful in guiding early treatment decisions. Healthcare providers should have a low threshold for initiating doxycycline whenever treating febrile or potentially septic patients from tribal lands in Arizona, even if an alternative diagnosis seems more likely and classic findings of RMSF are absent.
Background Rocky Mountain spotted fever (RMSF) has emerged as a significant cause of morbidity and mortality since 2002 on tribal lands in Arizona. The explosive nature of this outbreak and the recognition of an unexpected tick vector, Rhipicephalus sanguineus, prompted an investigation to characterize RMSF in this unique setting and compare RMSF cases to similar illnesses. Methods We compared medical records of 205 patients with RMSF and 175 with non-RMSF illnesses that prompted RMSF testing during 2002–2011 from 2 Indian reservations in Arizona. Results RMSF cases in Arizona occurred year-round and peaked later (July–September) than RMSF cases reported from other US regions. Cases were younger (median age, 11 years) and reported fever and rash less frequently, compared to cases from other US regions. Fever was present in 81% of cases but not significantly different from that in patients with non-RMSF illnesses. Classic laboratory abnormalities such as low sodium and platelet counts had small and subtle differences between cases and patients with non-RMSF illnesses. Imaging studies reflected the variability and complexity of the illness but proved unhelpful in clarifying the early diagnosis. Conclusions RMSF epidemiology in this region appears different than RMSF elsewhere in the United States. No specific pattern of signs, symptoms, or laboratory findings occurred with enough frequency to consistently differentiate RMSF from other illnesses. Due to the nonspecific and variable nature of RMSF presentations, clinicians in this region should aggressively treat febrile illnesses and sepsis with doxycycline for suspected RMSF.
We define the excess degree ξ(P ) of a d-polytope P as 2f 1 − df 0 , where f 0 and f 1 denote the number of vertices and edges, respectively. This parameter measures how much P deviates from being simple.It turns out that the excess degree of a d-polytope does not take every natural number: the smallest possible values are 0 and d − 2, and the value d − 1 only occurs when d = 3 or 5. On the other hand, for fixed d, the number of values not taken by the excess degree is finite if d is odd, and the number of even values not taken by the excess degree is finite if d is even.The excess degree is then applied in three different settings. It is used to show that polytopes with small excess (i.e. ξ(P ) < d) have a very particular structure: provided d = 5, either there is a unique nonsimple vertex, or every nonsimple vertex has degree d + 1. This implies that such polytopes behave in a similar manner to simple polytopes in terms of Minkowski decomposability: they are either decomposable or pyramidal, and their duals are always indecomposable. Secondly, we characterise completely the decomposable d-polytopes with 2d + 1 vertices (up to combinatorial equivalence). And thirdly all pairs (f 0 , f 1 ), for which there exists a 5-polytope with f 0 vertices and f 1 edges, are determined.sum of two polytopes Q + R is defined to be {x + y : x ∈ Q, y ∈ R}, and a polytope P is said to be homothetic to a polytope Q if Q = λP + t for λ > 0 and t ∈ R d . Polytopes with excess d − 2 exist in all dimensions, but their structure is quite restricted: either there is a unique nonsimple vertex, or there is a (d − 3)-face containing only vertices with excess degree one. Polytopes with excess d − 1 are in one sense even more restricted: they can exist only if d = 3 or 5. However a 5-polytope with excess 4 may also contain vertices with excess degree 2. On the other hand, d-polytopes with excess degree d or d + 2 are exceedingly numerous.In §5, we characterise all the decomposable d-polytopes with 2d + 1 or fewer vertices; this incidentally proves that a conditionally decomposable d-polytope must have at least 2d + 2 vertices.The final application, in §7, is the completion of the (f 0 , f 1 ) table for d ≤ 5; that is, we give all the possible values of (f 0 , f 1 ) for which there exists a d-polytope with d = 5, f 0 vertices and f 1 edges. The solution of this problem for d ≤ 4 was already well known [5, Chap. 10]. The same result has recently been independently obtained by Kusunoki and Murai [13]. Our proof requires some results of independent interest; in particular, a characterisation of the 4-polytopes with 10 vertices and minimum number of edges (namely, 21); this is completed in §6. We have more comprehensive results characterising polytopes with a given number of vertices and minimum possible number of edges, details of which will appear elsewhere [18].Most of our results tacitly assume that the dimension d is at least 3. When d = 2, all polytopes are both simple and simplicial, and the reader can easily see which theorems remain valid...
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