A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.Comment: 21 pages, 11 figures. v2 matches published version: improved presentation (including title, abstract and references), results and conclusions unchange

Common scale valuations across different preference-based measures: estimation using rank data

Background: Different preference-based measures (PBMs) used to estimate Quality Adjusted Life Years (QALYs) provide di¤erent utility values for the same patient. Differences are expected since values have been obtained using different samples, valuation techniques and descriptive systems. Previous studies have estimated the relationship between pairs of PBMs using patient self-reported data. However, there is a need for an approach capable of generating values directly on a common scale for a range of PBMs using the same sample of general population respondents and valuation technique but keeping the advantages of the different descriptive systems. Methods: General public survey data (n=501) where respondents ranked health states described using subsets of six PBMs were analysed. We develop a new model based on the mixed logit to overcome two key limitations of the standard rank ordered logit model, namely, the unrealistic choice pattern (Independence of Irrelevant Alternatives) and the independence of repeated observations. Results: There are substantial differences in the estimated parameters between the two models (mean di¤erence 0.07) leading to di¤erent orderings across the measures. Estimated values for the best states described by di¤erent PBMs are substantially and significantly di¤erent using the standard model, unlike our approach which yields more consistent results. Limitations: Data come from a exploratory study that is relatively small both in sample size and coverage of health states. Conclusions: This study develops a new, �exible econometric model specifically designed to reflect appropriately the features of rank data. Results support the view that the standard model is not appropriate in this setting and will yield very different and apparently inconsistent results. PBMs can be compared using a common scale by implementation of this new approach

A Radial Velocity Study of the Intermediate Polar EX Hydrae

A study on the intermediate polar EX Hya is presented, based on simultaneous photometry and high dispersion spectroscopic observations, during four consecutive nights. The strong photometric modulation related to with the 67-min spin period of the primary star is clearly present, as well as the narrow eclipses associated to the orbital modulation. Since our eclipse timings have been obtained almost 91,000 cycles since the last reported observations, we present new linear ephemeris, although we cannot rule out a sinusoidal variation suggested by previous authors. The system mainly shows double-peaked H$\alpha$, H$\beta$ and HeI $\lambda$5876 \AA emission lines. From the profile of the H$\alpha$ line, we find two components; one with a steep rise and velocities not larger than $\sim$1000 km s$^{-1}$ and another broader component extending up to $\sim$2000 km s$^{-1}$, which we interpret as coming mainly from the inner disc. A strong and variable hotspot is found and a stream-like structure is seen at times. We show that the best solution correspond to $K_1 = 58 \pm 5$ km s$^{-1}$ from H$\alpha$, from the two emission components, which are both in phase with the orbital modulation. We remark on a peculiar effect in the radial velocity curve around phase zero, which could be interpreted as a Rositter-MacLaughlin-like effect, which has been taken into account before deriving $K_1$. This value is compatible with the values found in high-resolution both in the ultraviolet and X-ray. We find: $M_{1} = 0.78 \pm 0.03$ M$_{\odot}$, $M_{2} = 0.10 \pm 0.02$ M$_{\odot}$ and $a = 0.67 \pm 0.01$ R$_{\odot}$. Doppler Tomography has been applied, to construct six Doppler tomograms for single orbital cycles spanning the four days of observations to support our conclusions. Our results indicate that EX Hya has a well formed disc and that the magnetosphere should extend only to about $3.75\,R_{\rm{WD}}$.Comment: 16 pages, 14 figures, accepted for publication in MNRA