Measuring infection transmission in a stochastic SIV model with infection reintroduction and imperfect vaccine

An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number $R_0$, which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, $R_0$ overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to $R_0$ are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic

Measuring infection transmission in a stochastic SIV model with infection reintroduction and imperfect vaccine

An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number $R_0$, which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, $R_0$ overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to $R_0$ are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic

Thickness of the buccal bone wall and root angulation in the maxilla and mandible: an approach to cone beam computed tomography

Background: The objective of this paper is to anatomically describe the bone morphology in the maxillary and mandibular tooth areas, which might help in planning post-extraction implants. Methods: CBCT images (Planmeca ProMax 3D) of 403 teeth (208 upper teeth and 195 lower teeth) were obtained from 49 patients referred to the Dental School of Seville from January to December 2014. The thickness of the facial wall was measured at the crest, point A, 4mm below, point B, and at the apex, point C. The second parameter was the angle formed between the dental axis and the axis of the basal bone. Results: A total of 403 teeth were measured. In the maxilla, 89.4% of incisors, 93.94% of canines, 78% of premolars and 70.5% of molars had a buccal bone wall thickness less than the ideal 2mm. In the mandible, 73.5% of incisors, 49% of canines, 64% of premolars and 53% of molars had <1mm buccal bone thickness as measured at point B. The mean angulation in the maxilla was 11.67±6.37° for incisors, 16.88±7.93° for canines, 13.93±8.6° for premolars, and 9.89±4.8° for molars. In the mandible, the mean values were 10.63±8.76° for incisors, 10.98±7.36° for canines, 10.54±5.82° for premolars and 16.19±11.22° for molars. Conclusions: The high incidence of a buccal wall thickness of less than 2mm in over 80% of the assessed sites indicates the need for additional regeneration procedures, and several locations may also require custom abutments to solve the angulation problems for screw-retained crowns

Outflows of hot molecular gas in ultra-luminous infra-red galaxies mapped with VLT-SINFONI

We present the detection and morphological characterization of hot molecular gas outflows in nearby ultra-luminous infrared galaxies, using the near-IR integral-field spectrograph SINFONI on the VLT. We detect outflows observed in the 2.12 micron H$_{2}$ 1-0 S(1) line for three out of four ULIRGs analyzed; IRAS 12112+0305, 14348-1447, and 22491-1808. The outflows are mapped on scales of 0.7-1.6 kpc, show typical outflow velocities of 300-500 km/s, and appear to originate from the nuclear region. The outflows comprise hot molecular gas masses of ~6-8x10$^3$ M(sun). Assuming a hot-to-cold molecular gas mass ratio of 6x10$^{-5}$, as found in nearby luminous IR galaxies, the total (hot+cold) molecular gas mass in these outflows is expected to be ~1x10$^{8}$ M(sun). This translates into molecular mass outflow rates of ~30-85 M(sun)/yr, which is a factor of a few lower than the star formation rate in these ULIRGs. In addition, most of the outflowing molecular gas does not reach the escape velocity of these merger systems, which implies that the bulk of the outflowing molecular gas is re-distributed within the system and thus remains available for future star formation. The fastest H$_{2}$ outflow is seen in the Compton-thick AGN of IRAS 14348-1447, reaching a maximum outflow velocity of ~900 km/s. Another ULIRG, IRAS 17208-0014, shows asymmetric H$_{2}$ line profiles different from the outflows seen in the other three ULIRGs. We discuss several alternative explanations for its line asymmetries, including a very gentle galactic wind, internal gas dynamics, low-velocity gas outside the disk, or two superposed gas disks. We do not detect the hot molecular counterpart to the outflow previously detected in CO(2-1) in IRAS 17208-0014, but we note that our SINFONI data are not sensitive enough to detect this outflow if it has a small hot-to-cold molecular gas mass ratio of < 9x10$^{-6}$.Comment: Accepted for publication in A&A (11 pages, 10 figures

On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics

In this paper, we revisit level-dependent quasi-birth-death processes with finitely many possible values of the level and phase variables by complementing the work of Gaver, Jacobs, and Latouche (Adv. Appl. Probab. 1984), where the emphasis is upon obtaining numerical methods for evaluating stationary probabilities and moments of first-passage times to higher and lower levels. We provide a matrix-analytic scheme for numerically computing hitting probabilities, the number of upcrossings, sojourn time analysis, and the random area under the level trajectory. Our algorithmic solution is inspired from Gaussian elimination, which is applicable in all our descriptors since the underlying rate matrices have a block-structured form. Using the results obtained, numerical examples are given in the context of varicella-zoster virus infections

Entropy maximization and the busy period of some single-server vacation models

In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T- and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable M/G/1 queueing models provides a parallel numerical study of the solution obtained via the maximum entropy approach versus “classical” solutions. The maximum entropy analysis of a continuous system descriptor (like the busy period) enriches the current body of literature which, in most cases, reduces to discrete queueing measures (such as the number of customers in the system)

Mid-infrared imaging- and spectro-polarimetric subarcsecond observations of NGC 1068

We present sub-arcsecond 7.5$-$13 $\mu$m imaging- and spectro-polarimetric observations of NGC 1068 using CanariCam on the 10.4-m Gran Telescopio CANARIAS. At all wavelengths, we find: (1) A 90 $\times$ 60 pc extended polarized feature in the northern ionization cone, with a uniform $\sim$44$^{\circ}$ polarization angle. Its polarization arises from dust and gas emission in the ionization cone, heated by the active nucleus and jet, and further extinguished by aligned dust grains in the host galaxy. The polarization spectrum of the jet-molecular cloud interaction at $\sim$24 pc from the core is highly polarized, and does not show a silicate feature, suggesting that the dust grains are different from those in the interstellar medium. (2) A southern polarized feature at $\sim$9.6 pc from the core. Its polarization arises from a dust emission component extinguished by a large concentration of dust in the galaxy disc. We cannot distinguish between dust emission from magnetically aligned dust grains directly heated by the jet close to the core, and aligned dust grains in the dusty obscuring material surrounding the central engine. Silicate-like grains reproduce the polarized dust emission in this feature, suggesting different dust compositions in both ionization cones. (3) An upper limit of polarization degree of 0.3 per cent in the core. Based on our polarization model, the expected polarization of the obscuring dusty material is $\lesssim$0.1 per cent in the 8$-$13 $\mu$m wavelength range. This low polarization may be arising from the passage of radiation through aligned dust grains in the shielded edges of the clumps.Comment: 17 pages, 10 figures, accepted for publication at MNRA

The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group

We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed

Near-Infrared Polarimetric Adaptive Optics Observations of NGC 1068: A torus created by a hydromagnetic outflow wind

We present J' and K' imaging linear polarimetric adaptive optics observations of NGC 1068 using MMT-Pol on the 6.5-m MMT. These observations allow us to study the torus from a magnetohydrodynamical (MHD) framework. In a 0.5" (30 pc) aperture at K', we find that polarisation arising from the passage of radiation from the inner edge of the torus through magnetically aligned dust grains in the clumps is the dominant polarisation mechanism, with an intrinsic polarisation of 7.0%$\pm$2.2%. This result yields a torus magnetic field strength in the range of 4$-$82 mG through paramagnetic alignment, and 139$^{+11}_{-20}$ mG through the Chandrasekhar-Fermi method. The measured position angle (P.A.) of polarisation at K$'$ is found to be similar to the P.A. of the obscuring dusty component at few parsec scales using infrared interferometric techniques. We show that the constant component of the magnetic field is responsible for the alignment of the dust grains, and aligned with the torus axis onto the plane of the sky. Adopting this magnetic field configuration and the physical conditions of the clumps in the MHD outflow wind model, we estimate a mass outflow rate $\le$0.17 M$_{\odot}$ yr$^{-1}$ at 0.4 pc from the central engine for those clumps showing near-infrared dichroism. The models used were able to create the torus in a timescale of $\geq$10$^{5}$ yr with a rotational velocity of $\leq$1228 km s$^{-1}$ at 0.4 pc. We conclude that the evolution, morphology and kinematics of the torus in NGC 1068 can be explained within a MHD framework.Comment: 14 pages, 4 figures, Accepted by MNRA