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In this article, we construct and analyse an Alternating Direction Implicit (ADI) scheme for singularly perturbed 2D parabolic convection–diffusion–reaction problems with two small parameters. We consider the operator-splitting ADI finite difference scheme for time stepping on a uniform mesh and a simple upwind-difference scheme for spatial discretization on a specially designed piecewise-uniform Shishkin mesh. The resulting scheme is proved to be uniformly convergent of order O (N − 1 ln ⁡ N + M − 1) , where N, M are the spatial and temporal parameters respectively. Numerical experiments confirm the theoretical results and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, a fully discrete numerical method is studied to solve the system of singularly perturbed parabolic convection–diffusion problem. The full discretization incorporates the backward-Euler method and the streamline-diffusion finite element method (SDFEM) for the temporal and spatial discretization, respectively. In each equation, the highest ordered spatial derivatives are multiplied by distinct parameters, hence the overlapping boundary layers phenomena displayed in the solution. To capture the singularity of the solution, a layer-adapted mesh has been used for the spatial domain discretization. The stability of the numerical method has been addressed by considering an appropriate stabilization parameter. A complete error analysis has shown the first order of accuracy of the fully discrete method in the discrete L 2 (0 , T ; S D) -norm. Lastly, few numerical experiments have been addressed to justify the theoretical estimates. [ABSTRACT FROM AUTHOR]

Abstract Background Staphylococcus aureus is part of normal flora and also an opportunistic pathogen responsible for a wide range of infections in both humans and animals. Livestock-associated S. aureus (LA-SA) has gained importance in recent years due to its increased prevalence in recent years, becoming a worry in public health view. This study aimed to study the epidemiology of LA-SA strains in Madurai district, Tamil Nadu, India. Methods A total of 255 samples were collected from bovine and other small ruminants like goats and sheep nares (n = 129 and n = 126 respectively). Nasal swab samples were collected from study animals with sterile sample collecting cotton swabs (Hi-Media, Mumbai). Samples were transported to the lab in Cary-Blair Transport media for further analysis. The samples were tested for S. aureus using antibiotic selection and PCR-based assays. The pathogenicity of the bacteria was assessed using chicken embryo models and liver cross-sections were used for histopathology studies. Results The prevalence rate in bovine-associated samples was 42.63% but relatively low in the case of small ruminants associated samples with 28.57% only. The overall prevalence of S. aureus is found to 35.6% and MRSA 10.98% among the study samples. The antibiogram results that LA-SA isolates were susceptible to aminoglycosides and tetracyclines but resistant to β-lactam drugs. The biofilm formation results showed that the LA-SA isolates are weak to high-capacity biofilm formers. The enterotoxigenic patterns revealed that most of the isolated strains are enterotoxigenic and possess classical enterotoxins. The survival analysis of chicken embryos suggested that the Bovine-associated strains were moderately pathogenic. Conclusion The study concluded that economically important livestock animals can act as reservoirs for multi-drug resistant and pathogenic which in-turn is a concern for public health as well as livestock health.