Brassicaceae is one of the most diverse and economically valuable angiosperm families with widely cultivated vegetable crops and scientifically important model plants, such as Arabidopsis thaliana. The evolutionary history, ecological, morphological, and genetic diversity, and abundant resources and knowledge of Brassicaceae make it an excellent model family for evolutionary studies. Recent phylogenetic analyses of the family revealed three major lineages (I, II, and III), but relationships among and within these lineages remain largely unclear. Here, we present a highly supported phylogeny with six major clades using nuclear markers from newly sequenced transcriptomes of 32 Brassicaceae species and large data sets from additional taxa for a total of 55 species spanning 29 out of 51 tribes. Clade A consisting of Lineage I and Macropodium nivale is sister to combined Clade B (with Lineage II and others) and a new Clade C. The ABC clade is sister to Clade D with species previously weakly associated with Lineage II and Clade E (Lineage III) is sister to the ABCD clade. Clade F (the tribe Aethionemeae) is sister to the remainder of the entire family. Molecular clock estimation reveals an early radiation of major clades near or shortly after the Eocene–Oligocene boundary and subsequent nested divergences of several tribes of the previously polytomous Expanded Lineage II. Reconstruction of ancestral morphological states during the Brassicaceae evolution indicates prevalent parallel (convergent) evolution of several traits over deep times across the entire family. These results form a foundation for future evolutionary analyses of structures and functions across Brassicaceae.

The expected cumulative health expenditures for healthier elderly persons, despite their greater longevity, were similar to those for less healthy persons. Health-promotion efforts aimed at persons under 65 years of age may improve the health and longevity of the elderly without increasing health expenditures.

To prevent the transmissions of malaria, dengue fever, or other mosquito-borne diseases, one of the effective weapons is the sterile insect technique in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population. To study the impact of the sterile insect technique on disease transmission, we formulate continuous-time mathematical models for the interactive dynamics of the wild and sterile mosquitoes, incorporating different strategies in releasing sterile mosquitoes. We investigate the model dynamics and compare the impact of the different release strategies. Numerical examples are also given to demonstrate rich dynamical features of the models.

The economic burden of hypertension is large, but health services directly related to hypertension account for only a fraction of attributed expenditures. Comprehensive accounting of expenditures more accurately assesses the cost of hypertension and potential savings from prevention and treatment. Alteration of lifestyles and medical intervention provide opportunities to reduce national health expenditures.

a b s t r a c tAn HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number R 0 . If R 0 ≤ 1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if R 0 > 1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

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Medical advances and the growth of the elderly population have focused interest on trends in the health of the elderly. Three theories have been advanced to describe these trends: compression of morbidity, expansion of morbidity, and dynamic equilibrium. We applied multistate life table methods to the Medicare Current Beneficiary Survey to estimate active and disabled life expectancy from 1992 to 2003, defining disability as having difficulty with instrumental activities of daily living or activities of daily living. We found increases in active life expectancy past age 65 and decreases in life expectancy with severe disability. These trends are consistent with elements of both the theory of compression of morbidity and the theory of dynamic equilibrium.

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