This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

Many studies have revealed the benefits of augmented reality (AR) to enhance productivity and fulfill a quality function in industry. Yet, the potential adverse effects of AR, such as physical stress, have not been extensively studied. This study investigates the effect of task difficulty (simple versus complex maintenance tasks) on the overall performance and physical stress of individuals while interacting with multimedia instructions (i.e., AR via HoloLens versus. paper-based guidance). Twenty-eight healthy male participants with a mean age of 32.12 years (standard deviation of 2.45 years) were randomly assigned to two groups: AR-based group and paper-based group. The metrics of total maintenance time, NASA-TLX scores, and heart rate variability (HRV) were used to evaluate overall performance, perceived workload, and physical stress, respectively. The findings suggest that AR-based instruction for a complex task significantly reduced both total maintenance time (by 14.94%) and physical stress in comparison with paper-based instruction. Paper-based instruction was found to destabilize heart rhythm, increase heart rate, and cause a shift in autonomic balance due to heightened sympathetic nerve activation. This study concludes that AR-based instruction is more efficient and less stressful than paper-based instruction, indicating that the AR system may offer independent benefits in reducing physical workloads.

American scientific publishing group

The objective of this paper is to evaluate the training efficiency of AR-based versus paper-based instruction methods with different levels of task complexity in terms of knowledge retention (i.e., short-term memory and long-term memory). Two maintenance operations were selected (i.e., low-demand (check all seals of the pump housing) and high-demand maintenance tasks (repair a gearbox of the piston pump and check all seals of the gearbox)). Twenty-eight healthy males were recruited and randomly divided into two groups. Each participant performed the maintenance task with assistance (i.e., AR-based or paper-based instruction) and repeated it without instructions twice (30 min apart and then two weeks later). Knowledge retention was measured using the total task completion time without guidance, error number, the number of self-corrected errors (SCEs), and the number of times help was sought from the researcher. The results show that using AR-based instruction enhanced the participants’ performance, especially in the highly demanding task, by reducing task completion time and errors in both short- and long-term retention tasks. Participants who were guided through a paper-based instruction method showed more errors, more instances of seeking help from the researcher, and a longer time to complete the long-term retention task, compared with those guided through the AR-based instruction method. Overall, using AR instruction to guide maintenance workers increased training transfer by 33.61%.