Mathematical Model of Vaccine Noncompliance

Vaccine scares can prevent individuals from complying with a vaccination program. When compliance is high, the critical vaccination proportion is close to being met, and herd immunity occurs, bringing the disease incidence to extremely low levels. Thus, the risk to vaccinate may seem greater than the risk of contracting the disease, inciting vaccine noncompliance. A previous behavior-incidence ordinary differential equation model shows both social learning and feedback contributing to changes in vaccinating behavior, where social learning is the perceived risk of vaccinating and feedback repre- sents new cases of the disease. In our study, we compared several candidate models to more simply illustrate both vaccination coverage and incidence through social learn- ing and feedback. The behavior model uses logistic growth and exponential decay to describe the social learning aspect as well as different functional forms of the disease prevalence to represent feedback. Each candidate model was tested by fitting it to data from the pertussis vaccine scare in England and Wales in the 1970s. Our most parsimonious model shows a superior fit to the vaccine coverage curve during the scare

On positivity and base loci of vector bundles

The aim of this note is to shed some light on the relationships among some notions of positivity for vector bundles that arose in recent decades. Our purpose is to study several of the positivity notions studied for vector bundles with some notions of asymptotic base loci that can be defined on the variety itself, rather than on the projectivization of the given vector bundle. We relate some of the different notions conjectured to be equivalent with the help of these base loci, and we show that these can help simplify the various relationships between the positivity properties present in the literature. In particular, we define augmented and restricted base loci $\mathbb{B}_+ (E)$ and $\mathbb{B}_- (E)$ of a vector bundle $E$ on the variety $X$, as generalizations of the corresponding notions studied extensively for line bundles. As it turns out, the asymptotic base loci defined here behave well with respect to the natural map induced by the projectivization of the vector bundle $E$

MEMS 411: Portable Bridge Crane

The team designed and built a portable bridge crane for use in class demonstrations. The design was be based off a typical gantry crane, which consists of a trolley spanning across two horizontal parallel beams that are part of a gantry with a payload hanging from the trolley. The group also needed to design the gantry itself and ensure it was both stable enough to support the trolley and payload at the desired operation speeds as well as scaled properly for the desired use

Characterization of Vemurafenib Phototoxicity in a Mouse Model

Vemurafenib is a first-in-class, small molecule B-Raf kinase inhibitor for the treatment of patients with unresectable or metastatic melanoma carrying the BRAFV600E mutation, commercially available since 2011. A general phototoxic potential was identified early during development; however, based on results of an animal study in hairless rats, it was concluded that there would exist no relevant risk for humans. Surprisingly, signs of clinical photosensitivity were reported in many patients during clinical development. Therefore, it became a fundamental question to understand this discrepancy. An established mouse model (oral UV-Local Lymph Node Assay, UV-LLNA) for the assessment of in vivo photosafety was used to investigate the impact of formulations, dose levels, duration of treatment, and timing of irradiation. Moreover, a basic pharmacokinetic profile was established within the same mouse strain. We were able to demonstrate dose- and time-dependent phototoxicity of vemurafenib using commercially available tablets (stabilized amorphous material). The lowest phototoxic dose was 350mg/kg administrated for 3 consecutive days followed by exposure to UV-visible irradiation at a UVA-normalized dose of 10 J/cm2. In comparison, pure vemurafenib, which easily forms crystalline variants and is known to have poor bioavailability, was tested at 350mg/kg, and no signs of phototoxicity could be seen. The most apparent difference between the early study in hairless rats and this study in mice was the spectral range of the irradiation light source (350-400nm vs 320-700nm). Because vemurafenib does not absorb sufficiently light above 350nm, this difference can easily explain the negative earlier study result in hairless rat