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Mathematical models are among the most successful strategies for predicting the dynamics of a disease spreading in a population. Among them, the so-called compartmental models, where the total population is proportionally divided into compartments, are widely used. The SIR model (Susceptible-Infected-Recovered) is one of them, where the dynamics between the compartments follows a system of nonlinear differential equations. As a result of the non-linearity of the SIR dynamics, it has no analytical solution. Therefore, some numerical methods must be used to obtain an approximate solution. In this contribution, we present simulated scenarios for the SIR model showing its stiffness, a phenomenon that implies the necessity of a small step size choice in the numerical approximation. The numerical results, in particular, show that the stiffness phenomenon increases with higher transmission rates and lower birth and mortality rates . We compare the numerical solutions and errors for the SIR model using explicit Euler, Runge Kutta, and the semi-implicit Rosenbrock methods and analyze the numerical implications of the stiffness on them. As a result, we conclude that any accurate numerical solution of the SIR model will depend on an appropriately chosen numerical method and the time step, in terms of the values of the parameters.

Since influenza is a seasonal mutating disease, in this paper, we propose and analyze a multi-fractional version of the SIRC model (which relates the S-susceptible, I-Infected, R-recovered, and C-cross-immune individuals in the population N) to capture the immunological memory gained by individuals that have previous contact Influenza strains. We show the well-posedness and consistency of the proposed multi-fractional dynamics and analyze the stability of stationary points with an analytical/numerical strategy. The simulated scenarios show that the proposed model describes more precisely reported Influenza H1N1 data, from the State of Rio Grande do Sul, in the year 2010. Moreover, it shows that the memory enhanced by the fractional dynamics (that model the immunological memory) implies a substantial decrease of susceptibility of re-infection by strain mutations in long-running diseases, but is larger in the beginning.

Em um contexto em que se promove o uso de metodologias ativas, estratégias e planejamentos de aulas aliados à tecnologia, entre outras muitas ferramentas tão significativas para disponibilizar um ambiente propício ao desenvolvimento de um aprendizado eficaz, questiona-se por que nossos alunos não alcançam os objetivos propostos. O que é necessário de fato para que o processo de ensino/aprendizagem seja eficaz e torne o aluno um indivíduo autônomo? O problema talvez não esteja somente no aluno. Será que o professor, mesmo tendo capacitação profissional para atuar na sua área, teve as orientações e a formação acadêmica necessária para trazer aos alunos métodos e ferramentas para as mais amplas possibilidades de melhorarem seu universo do conhecimento? Nesse contexto, esse trabalho tem o objetivo de trazer uma reflexão sobre a formação docente de maneira a atender a demanda no contexto atual da educação, somado ao ato pedagógico que incentive no professor a autonomia que muitas vezes ele deve instigar em seus alunos, mas devido à falta de motivação e atuação do “ser professor” não consegue desenvolver as habilidades que a educação exige.

Background: Medically unexplained symptoms otherwise referred to as persistent physical symptoms (PPS) are debilitating to patients. As many specific PPS syndromes share common behavioural, cognitive, and affective influences, transdiagnostic treatments might be effective for this patient group. We evaluated the clinical efficacy and cost-effectiveness of a therapist-delivered, transdiagnostic cognitive behavioural intervention (TDT-CBT) plus (+) standard medical care (SMC) v. SMC alone for the treatment of patients with PPS in secondary medical care. Methods: A two-arm randomised controlled trial, with measurements taken at baseline and at 9, 20, 40- and 52-weeks post randomisation. The primary outcome measure was the Work and Social Adjustment Scale (WSAS) at 52 weeks. Secondary outcomes included mood (PHQ-9 and GAD-7), symptom severity (PHQ-15), global measure of change (CGI), and the Persistent Physical Symptoms Questionnaire (PPSQ). Results: We randomised 324 patients and 74% were followed up at 52 weeks. The difference between groups was not statistically significant for the primary outcome (WSAS at 52 weeks: estimated difference −1.48 points, 95% confidence interval from −3.44 to 0.48, p = 0.139). However, the results indicated that some secondary outcomes had a treatment effect in favour of TDT-CBT + SMC with three outcomes showing a statistically significant difference between groups. These were WSAS at 20 weeks (p = 0.016) at the end of treatment and the PHQ-15 (p = 0.013) and CGI at 52 weeks (p = 0.011). Conclusion: We have preliminary evidence that TDT-CBT + SMC may be helpful for people with a range of PPS. However, further study is required to maximise or maintain effects seen at end of treatment. [ABSTRACT FROM AUTHOR]

Objective: To contribute to an optimised training programme for care staff that supports the implementation of evidence-based psychosocial interventions in long-term care.Methods: Qualitative study that involved focus group discussions with 119 care home staff within 16 care homes in the UK. Part of wider clinical trial aimed at developing and evaluating an effective and practical psychosocial intervention and implementation approach for people with dementia in long-term care. Inductive thematic analysis was used to identify themes and interpret the data.Results: The findings highlighted that successful training and support interventions must acknowledge and respond to 'whole home' issues. Three overarching themes emerged as influential: the importance of contextual factors such as staff morale, interpersonal relationships within the home, and experience and perceived value of the proposed intervention.Conclusions: Priority must be given to obtain the commitment of all staff, management and relatives to the training programme and ensure that expectations regarding interaction with residents, participation in activities and the reduction of medication are shared across the care home. [ABSTRACT FROM AUTHOR]

Objectives Emerging literature suggests that lifestyle factors may play an important role in reducing age-related cognitive decline. There have, however, been few studies investigating the role of cognitively stimulating leisure activities in maintaining cognitive health. This study sought to identify changes in cognitive performance with age and to investigate associations of cognitive performance with several key cognitively stimulating leisure activities. Method Over 65,000 participants provided demographic and lifestyle information and completed tests of grammatical reasoning, spatial working memory, verbal working memory and episodic memory. Results Regression analyses suggested that frequency of engaging in Sudoku or similar puzzles was significantly positively associated with grammatical reasoning, spatial working memory and episodic memory scores. Furthermore, for participants aged under 65 years, frequency of playing non-cognitive training computer games was also positively associated with performance in the same cognitive domains. The results also suggest that grammatical reasoning and episodic memory are particularly vulnerable to age-related decline. Further investigation to determine the potential benefits of participating in Sudoku puzzles and non-cognitive computer games is indicated, particularly as they are associated with grammatical reasoning and episodic memory, cognitive domains found to be strongly associated with age-related cognitive decline. Conclusions Results of this study have implications for developing improved guidance for the public regarding the potential value of cognitively stimulating leisure activities. The results also suggest that grammatical reasoning and episodic memory should be targeted in developing appropriate outcome measures to assess efficacy of future interventions, and in developing cognitive training programmes to prevent or delay cognitive decline. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Background: Patients continue to suffer from medically unexplained symptoms otherwise referred to as persistent physical symptoms (PPS). General practitioners (GPs) play a key role in the management of PPS and require further training. Patients are often frustrated with the care they receive. This study aims to assess the acceptability of an 'integrated GP care' approach which consists of offering self-help materials to patients with PPS and offering their GPs training on how to utilise cognitive behavioural skills within their consultations, as well as assessing the feasibility of conducting a future trial in primary care to evaluate its benefit. Methods: A feasibility cluster randomised controlled trial was conducted in primary care, South London, UK. GP practices (clusters) were randomly allocated to 'integrated GP care plus treatment as usual' or 'treatment as usual'. Patients with PPS were recruited from participating GP practices before randomisation. Feasibility parameters, process variables and potential outcome measures were collected at pre-randomisation and at 12- and 24-weeks post-randomisation at cluster and individual participant level. Results: Two thousand nine hundred seventy-eight patients were identified from 18 GP practices. Out of the 424 patients who responded with interest in the study, 164 fully met the eligibility criteria. One hundred sixty-one patients provided baseline data before cluster randomisation and therefore were able to participate in the study. Most feasibility parameters indicated that the intervention was acceptable and a future trial feasible. 50 GPs from 8 GP practices (randomised to intervention) attended the offer of training and provided positive feedback. Scores in GP knowledge and confidence increased post-training. Follow-up rate of patients at 24 weeks was 87%. However estimated effect sizes on potential clinical outcomes were small. Conclusions: It was feasible to identify and recruit patients with PPS. Retention rates of participants up to 24 weeks were high. A wide range of health services were used. The intervention was relatively low cost and low risk. This complex intervention should be further developed to improve patients'/GPs' utilisation of audio/visual and training resources before proceeding to a full trial evaluation. Trial registration: NCT02444520 (ClinicalTrials.gov). [ABSTRACT FROM AUTHOR]