GLOBAL STABILITY AND BIFURCATIONS ANALYSIS OF AN EPIDEMIC MODEL WITH CONSTANT REMOVAL RATE OF THE INFECTIVE

In this thesis we consider an epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infective on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation. Keyword: Epidemic model, nonlinear incidence rate, basic reproduction number, local and global stabilit

The planarity of the stickface motion in the field hockey hit

The field hockey hit is an important but poorly understood stroke. This study investigated the planarity of the stickface motion during the downswing, in order to better characterise the kinematics and to assess the suitability of planar pendulum models for simulating the hit. Thirteen experienced female field hockey players were filmed executing hits with a single approach step, and the kinematics of the centre of the stickface were measured. A method was developed for identifying how far back from impact the stickface motion was planar. Orthogonal least-squares regression was used to determine best-fit planes for sections of the stickface path of varying length, each of which ended at impact, and these sections were considered planar if the mean residual between the stickface path and the fitted plane was less than 0.25% of the distance traveled by the stickface during that period. On average the stickface motion was planar for the last 83±12% of its downswing path, with the length of the planar section ranging from 1.85 m to 2.70 m. The suitability of a planar model for the stickface motion was supported, but further investigation of the stick and arm kinematics is warranted

The planarity of the stickface motion in the field hockey hit

The field hockey hit is an important but poorly understood stroke. This study investigated the planarity of the stickface motion during the downswing, in order to better characterise the kinematics and to assess the suitability of planar pendulum models for simulating the hit. Thirteen experienced female field hockey players were filmed executing hits with a single approach step, and the kinematics of the centre of the stickface were measured. A method was developed for identifying how far back from impact the stickface motion was planar. Orthogonal least-squares regression was used to determine best-fit planes for sections of the stickface path of varying length, each of which ended at impact, and these sections were considered planar if the mean residual between the stickface path and the fitted plane was less than 0.25% of the distance traveled by the stickface during that period. On average the stickface motion was planar for the last 83±12% of its downswing path, with the length of the planar section ranging from 1.85 m to 2.70 m. The suitability of a planar model for the stickface motion was supported, but further investigation of the stick and arm kinematics is warranted

Comparison of Two Methods for In Vivo Estimation of the Glenohumeral Joint Rotation Center (GH-JRC) of the Patients with Shoulder Hemiarthroplasty

Determination of an accurate glenohumeral-joint rotation center (GH-JRC) from marker data is essential for kinematic and dynamic analysis of shoulder motions. Previous studies have focused on the evaluation of the different functional methods for the estimation of the GH-JRC for healthy subjects. The goal of this paper is to compare two widely used functional methods, namely the instantaneous helical axis (IHA) and symmetrical center of rotation (SCoRE) methods, for estimating the GH-JRC in vivo for patients with implanted shoulder hemiarthroplasty. The motion data of five patients were recorded while performing three different dynamic motions (circumduction, abduction, and forward flexion). The GH-JRC was determined using the CT-images of the subjects (geometric GH-JRC) and was also estimated using the two IHA and SCoRE methods. The rotation centers determined using the IHA and SCoRE methods were on average 1.47±0.62 cm and 2.07±0.55 cm away from geometric GH-JRC, respectively. The two methods differed significantly (two-tailed p-value from paired t-Test ∼0.02, post-hoc power ∼0.30). The SCoRE method showed a significant lower (two-tailed p-value from paired t-Test ∼0.03, post-hoc power ∼0.68) repeatability error calculated between the different trials of each motion and each subject and averaged across all measured subjects (0.62±0.10 cm for IHA vs. 0.43±0.12 cm for SCoRE). It is concluded that the SCoRE appeared to be a more repeatable method whereas the IHA method resulted in a more accurate estimation of the GH-JRC for patients with endoprostheses

The instantaneous helical axis of the subtalar and talocrural joints: a non-invasive in vivo dynamic study

<p>Abstract</p> <p>Background</p> <p>An understanding of rear-foot (talocrural and subtalar joints) kinematics is critical for diagnosing foot pathologies, designing total ankle implants, treating rear-foot injuries and quantifying gait abnormalities. The majority of kinematic data available have been acquired through static cadaver work or passive <it>in vivo </it>studies. The applicability of these data to dynamic <it>in vivo </it>situations remains unknown. Thus, the purpose of this study was to fully quantify subtalar, talocrural and calcaneal-tibial <it>in vivo </it>kinematics in terms of the instantaneous helical axis (IHA) in twenty-five healthy ankles during a volitional activity that simulated single-leg toe-raises with partial-weight support, requiring active muscle control.</p> <p>Methods</p> <p>Subjects were each placed supine in a 1.5 T MRI and asked to repeat this simulated toe-raise while a full sagittal-cine-phase contrast (dynamic) MRI dataset was acquired. From the cine-phase contrast velocity a full kinematic description for each joint was derived.</p> <p>Results</p> <p>Nearly all motion quantified at the calcaneal-tibial joint was attributable to the talocrural joint. The subtalar IHA orientation and position were highly variable; whereas, the talocrural IHA orientation and position were extremely consistent.</p> <p>Conclusion</p> <p>The talocrural was well described by the IHA and could be modeled as a fixed-hinge joint, whereas the subtalar could not be.</p

Activity profile of top-class association football referees in relation to fitness test performance and match standard

The aim of this study was to examine the kinematic activity profiles, cardiovascular responses and physical fitness of top-class football referees (n=11) during the FIFA Confederations Cup 2005. Computerised match-analyses (n=9) were performed with a two-dimensional photogrammetric video system, and the cardiovascular demand imposed on the referees (n=12) was measured using heart rate recordings. Total distance covered was 10,218, s=643 m of which 3531, s=510 m was covered at high intensities (>3.6 m.s(-1)). Both total distance covered (r2=0.59; P=0.02) and high-intensity activities (r2=0.44; P=0.05) were related to the distance covered by the ball in the same match. The referees ran at high speed 37% further (P=0.01) in the actual tournament than during under-17 top-level officiating. After the 5-min interval during which high-speed running peaked, in the following 5 min the performance was reduced by 19% (P=0.01) in relation to the mean of the game. Mean heart rate was 161, s=9 b.min(-1) (86, s=3% of maximal heart rate (HRmax)). Mean heart rate (expressed as percentage of HRmax) was related in part (r2=0.36; P5 m.s(-1)) best describes the physical performance of referees; (3) heart rate recording can be a useful tool to determine the most intense periods of a match and (4) the new fitness tests adopted by FIFA were poor predictors of match activities