Travelling waves for an epidemic model with non-smooth treatment rates

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOP Publishing Ltd and SISSA.We consider a susceptible–infected–removed (SIR) epidemic model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For case (i), we compute travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infective state or two endemic states with each other. For case (ii), it is shown that the profile has the following properties: the number of susceptibles is monotonically increasing and the number of infectives approaches zero at infinity, while their product converges to a constant. Numerical simulations are performed for all these cases. Abnormal behaviour like travelling waves with non-monotonic profile or oscillations is observed

Qualitative assessment of the role of public health education program on HIV transmission dynamics

© The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.This paper presents a nonlinear deterministic model for assessing the impact of public health education campaign on curtailing the spread of the HIV pandemic in a population. Rigorous qualitative analysis of the model reveals that it exhibits the phenomenon of backward bifurcation (BB), where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the 'effective reproduction number' (Reff), is less than unity. The epidemiological implication of BB is that a public health education campaign could fail to effectively control HIV, even when the classical requirement of having the associated reproduction number less than unity is satisfied. Furthermore, an explicit threshold value is derived above which such an education campaign could lead to detrimental outcome (increase disease burden), and below which it would have positive population-level impact (reduce disease burden in the community). It is shown that the BB phenomenon is caused by imperfect efficacy of the public health education program. The model is used to assess the potential impact of some targeted public health education campaigns using data from numerous countries.Kano State Government of Nigeria (N.H.); Natural Science and Engineering Research Council and Mathematics of Information Technology and Complex Systems of Canada (A.B.G.

Modelling the dynamics of Chikungunya in human and mosquito populations

In this paper, we developed and qualitatively analyzed a model for the transmissiondynamics of chikungunya virus in a human a nd mosquito populations. The chikungunyavirus is transmitted by Aedes mosquitoes usually Aedes albopictus mosquito and it is of bigthreat to global public health. Rigorous analysis of the model shows that the model has alocally asymptotically stable disease free equilibrium whenever a certain epidemiologicalthreshold quantity, called the basic reproduction number is less than unity (hence, thediseases would not persist in the community). The model has a unique endemicequilibrium when the reproduction number exceeds unity. Furthermore, the model exhibitsthe phenomenon of backward bifurcation, where the stable disease free equilibriumcoexists with a stable endemic equilibrium.Keywords: Chikungunya virus; vertical transmission; stability; backward bifurcation

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented

Growth and characterizations of bis glycine hydrogen bromide (BGHB) single crystal: new nonlinear optical material

Growth and characterization of new nonlinear optical material bis glycine hydrogen bromide is reported in the present communication. Single crystals of bis glycine hydrogen bromide was grown from solution by slow evaporation technique. The grown crystals were characterized by single crystal X-ray diffraction analysis, to confirm the crystal structure and to measure cell parameters. The presence of functional groups and coordination of glycine group with hydro bromic acid were confirmed by FTIR, UV-visible and absorbance spectrum was recorded to study the transparency of grown crystals. The bis glycine hydrogen bromide crystal does not decompose before melting. This was confirmed by thermo gravimetric analysis (TGA). The second order nonlinear optical property of the grown crystal was confirmed by Kurtz and Perry powder SHG test.Â

Effective Temperatures of Low-Mass Stars from High-Resolution H-band Spectroscopy

High-resolution, near-infrared spectra will be the primary tool for finding and characterizing Earth-like planets around low-mass stars. Yet, the properties of exoplanets can not be precisely determined without accurate and precise measurements of the host star. Spectra obtained with the Immersion GRating INfrared Spectrometer (IGRINS) simultaneously provide diagnostics for most stellar parameters, but the first step in any analysis is the determination of the effective temperature. Here we report the calibration of high-resolution H-band spectra to accurately determine effective temperature for stars between 4000-3000 K ($\sim$K8--M5) using absorption line depths of Fe I, OH, and Al I. The field star sample used here contains 254 K and M stars with temperatures derived using BT-Settl synthetic spectra. We use 106 stars with precise temperatures in the literature to calibrate our method with typical errors of about 140 K, and systematic uncertainties less than $\sim$120 K. For the broadest applicability, we present T$_{\rm eff}$--line-depth-ratio relationships, which we test on 12 members of the TW Hydrae Association and at spectral resolving powers between $\sim$10,000--120,000. These ratios offer a simple but accurate measure of effective temperature in cool stars that is distance and reddening independent.Comment: 19 pages, 11 figures and 3 tables. Accepted in Ap

Drug utilization review of anticancer drugs in cancer outpatient department of the Government Medical College, Aurangabad

Background: To study drug utilization of anticancer drugs in cancer outpatient department (OPD) of Government Medical College, Aurangabad.Methods: Five hundred and twelve prescription records were screened and analyzed as per the study parameters from cancer OPD of Government Medical College and Hospital, Aurangabad. Commonly used anticancer drugs were recorded; furthermore, different types of carcinomas were noted.Results: Age group of patients was in between 30 and 70, 267 were females and 245 were male patients. The most common type of carcinoma was carcinoma of the breast (17.9%). Carboplatin was the most commonly used anticancer drug (26.56%). The average number of anticancer drugs received per patient was three.Conclusion: WHO suggested drug utilization studies are needed in every health care setting. For a developing country like India, National Drug Policy and Drugs and Therapeutic Committee are a must

Computation of Kolmogorov's Constant in Magnetohydrodynamic Turbulence

In this paper we calculate Kolmogorov's constant for magnetohydrodynamic turbulence to one loop order in perturbation theory using the direct interaction approximation technique of Kraichnan. We have computed the constants for various $E^u(k)/E^b(k)$, i.e., fluid to magnetic energy ratios when the normalized cross helicity is zero. We find that $K$ increases from 1.47 to 4.12 as we go from fully fluid case $(E^b=0)$ to a situation when $E^u/E^b=0.5$, then it decreases to 3.55 in a fully magnetic limit $(E^u=0)$. When $E^u/E^b=1$, we find that $K=3.43$.Comment: Latex, 10 pages, no figures, To appear in Euro. Phys. Lett., 199

Effect of COVID-19 quarantine on the sleep quality and the depressive symptom levels of university students in Jordan during the spring of 2020

Objectives: This study was designed to assess the effect of COVID-19 home quarantine and its lifestyle challenges on the sleep quality and mental health of a large sample of undergraduate University students in Jordan. It is the first study applied to the Jordanian population. The aim was to investigate how quarantine for several weeks changed the students' habits and affected their mental health. Methods: A cross-sectional study was conducted using a random representative sample of 6,157 undergraduate students (mean age 19.79 ± 1.67 years, males 28.7%) from the University of Jordan through voluntarily filling an online questionnaire. The Pittsburgh Sleep Quality Index (PSQI) and the Center for Epidemiologic Studies-Depression Scale (CES-D) were used to assess sleep quality and depressive symptoms, respectively. Results: The PSQI mean score for the study participants was 8.1 ± 3.6. The sleep quality of three-quarters of the participants was negatively affected by the extended quarantine. Nearly half of the participants reported poor sleep quality. The prevalence of poor sleep quality among participants was 76% (males: 71.5% and females: 77.8%). Similarly, the prevalence of the depressive symptoms was 71% (34% for moderate and 37% for high depressive symptoms), with females showing higher prevalence than males. The overall mean CES-D score for the group with low depressive symptoms is 9.3, for the moderate group is 19.8, while it is 34.3 for the high depressive symptoms group. More than half of the students (62.5%) reported that the quarantine had a negative effect on their mental health. Finally, females, smokers, and students with decreased income levels during the extended quarantine were the common exposures that are significantly associated with a higher risk of developing sleep disturbances and depressive symptoms. Conclusions: Mass and extended quarantine succeeded in controlling the spread of the COVID-19 virus; however, it comes with a high cost of potential psychological impacts. Most of the students reported that they suffer from sleeping disorders and had a degree of depressive symptoms. Officials should provide psychological support and clear guidance to help the general public to reduce these potential effects and overcome the quarantine period with minimum negative impacts

Characterization of semi-refined carrageenan film plasticized with glycerol incorporated with Persicaria minor extract as antioxidant additives

Semi refined carrageenan (2%w/w) plasticized with 0.9% (w/w) glycerol (G) added with Persicaria minor (PM) extract and 0.4% (w/w) BHA as antioxidant additives for the development of active packaging films. The extraction of PM using 75% (v/v) ethanol: water ratio showed the highest polyphenol content with 176.80±4.37 Gallic Acid Equivalent (GAE)/L sample and 94.65±0.17% inhibition analyzed using DPPH antioxidant activity (p<0.05). The characterization of SRC-G based film containing 0.4, 1.0, 1.5 and 2.0% (w/w) PM and BHA were observed using FTIR, mechanical and physical properties of the treated films. FTIR spectrum band showed insight analysis of PM extract and BHA with carrageenan. SRC film plasticized with glycerol improved overall physical properties including thickness, barrier and flexibility and increased tensile strength and elongation at break compared to the SRC film only (p<0.05). The active films with PM extracts (2.0% w/w) exhibited good mechanical properties with tensile strength and elongation at break with 28.01±0.17 and 37.37±0.29 respectively (p<0.05). The addition of PM extract in SRC films increased the moisture content and opacity as proportionally to the concentration of PM extracts. Film treated with 2.0% PM showed lowest value of films solubility compare to all sample (p<0.05). Hence, the characterization measurement of SRC based films demonstrated great potential with natural extract formulation for the development of active film packaging for food products