Articles

This article presents a mathematical model designed to simulate the impact of targeted interventions aimed at preventing HIV transmission among female sex workers (FSWs) and their clients, while also analyzing their effects on the health of the general population. The compartmental model distinguishes between high-risk populations (FSWs and their clients) and low-risk populations (sexually active men and women in the general population), and links prevention efforts in high-risk groups to the evolution of the epidemic in the low-risk population. The fundamental properties of the model, such as the positivity of solutions and the boundedness of the system, have been verified, and the basic reproduction number R<SUB>0</SUB> has been calculated. Finally, the stability of the model was studied using Varga’s theorem and the Lyapunov method. Simulation results show that targeted prevention among FSWs and their clients reduces HIV incidence in the general population. This framework provides a valuable tool for guiding policymakers in the design of effective strategies to combat the epidemic, especially relevant in the context of suspension of USAID funding.

We study a dynamic model of the relationship between two people where the states depend on the “power” in the relationship. We perform a comprehensive analysis of stability of the system, and determine a set of conditions under which stable relationships are possible. In particular, stable relationships can occur if both people are dominant, but the sum of dominances is below a bound determined by the model’s parameters. Stable relationships can also occur if one person is dominant and the other is submissive, provided the level of dominance exceeds the level of submissiveness but not beyond a threshold. We also conclude that a stable relationship is not possible if both people are submissive. While our model is motivated by a social or romantic relationship, it can also be applied to professional or business relationships, diplomatic relationships between nations, and certain biological interactions between organisms and between automated agents or robots.

The characterization of rock mass along the tunnel alignment based on physical, geological and geotechnical data of the project area was used in this work. The support systems were recommended for all geotechnical units using RMR and tunneling quality index (Q-system) support chart. The paper also consists in making a two-dimensional numerical study of the stability of the left lateral slope of the Portal of the tunnel with the Slide 6.0 software and inside provisional support with the Phase.2 2D program. The study shows good results of the internal rock mass stability of the tunnel and satisfactory safety factor (FoS) in terms of collapse analyzes of the lateral slope of the tunnel portals.

<b>Objective: </b>The effects of muscle fatigue appear to elicit a transient means of postural instability; however, the recovery of postural stability after fatiguing exercise has not been extensively studied. This study aimed to determine the immediate effect of local vibration applied to fatigued plantar flexor muscles on postural stability in healthy young adults. <b>Design: </b>True Experimental (pre-test - post test design with a control group). <b>Setting:</b> A tertiary care centre. <b>Participations:</b> 42 healthy young adults. <b>Intervention:</b> Fatigue of plantar flexors muscles was induced by repeated dynamic contractions performed to maximum exhaustion. Experimental group (n= 21) received local vibration to fatigued muscles with a handheld vibrator whereas the control group (n = 21) received no intervention (rest). Postural stability was assessed using one leg stance test (OLST) under three different conditions viz. pre-fatigue, post-fatigue and post rest/vibration. <b>Results: </b>Comparative analysis of postural stability within the group was done pre-fatigue, post-fatigue and post rest/vibration condition using Kruskal-Wallis test. A significant decrease from pre-fatigue to post-fatigue condition (p-value < 0.001); and a significant increase from post-fatigue to post rest/vibration condition (p-value < 0.001) was observed in OLST in both - control group and experimental group. However, further comparison of OLST between the groups (using unpaired t test) showed a significant difference in post-fatigue condition versus post rest/vibration condition in favour of the experimental group. <b>Conclusion: </b>Plantar flexors fatigue significantly affects one leg stance time in healthy young adults. Results of this study show that there is an immediate effect of vibration to fatigued muscles on recovery of postural stability in healthy young adults. Recovery of postural stability achieved quickly with such a simple tool may help increase the degree of participation in sports and other similar activities which can cause muscles to fatigue. However, more studies are required to determine this effect using other clinical measures.