Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Report 46: Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals.

The SARS-CoV-2 Gamma variant spread rapidly across Brazil, causing substantial infection and death waves. We use individual-level patient records following hospitalisation with suspected or confirmed COVID-19 to document the extensive shocks in hospital fatality rates that followed Gamma's spread across 14 state capitals, and in which more than half of hospitalised patients died over sustained time periods. We show that extensive fluctuations in COVID-19 in-hospital fatality rates also existed prior to Gamma's detection, and were largely transient after Gamma's detection, subsiding with hospital demand. Using a Bayesian fatality rate model, we find that the geographic and temporal fluctuations in Brazil's COVID-19 in-hospital fatality rates are primarily associated with geographic inequities and shortages in healthcare capacity. We project that approximately half of Brazil's COVID-19 deaths in hospitals could have been avoided without pre-pandemic geographic inequities and without pandemic healthcare pressure. Our results suggest that investments in healthcare resources, healthcare optimization, and pandemic preparedness are critical to minimize population wide mortality and morbidity caused by highly transmissible and deadly pathogens such as SARS-CoV-2, especially in low- and middle-income countries. NOTE: The following manuscript has appeared as 'Report 46 - Factors driving extensive spatial and temporal fluctuations in COVID-19 fatality rates in Brazilian hospitals' at https://spiral.imperial.ac.uk:8443/handle/10044/1/91875 . ONE SENTENCE SUMMARY: COVID-19 in-hospital fatality rates fluctuate dramatically in Brazil, and these fluctuations are primarily associated with geographic inequities and shortages in healthcare capacity

Toothache and associated factors in Brazilian adults: a cross-sectional population-based study

Extent: 8p.Background: Toothache is a dental public health problem and one of the predictors of dental attendance and it is strongly associated with the life quality of individuals. In spite of this, there are few population-based epidemiological studies on this theme. Objective: To estimate the prevalence of toothache and associated factors in adults of Lages, Southern Brazil. Methods: A cross-sectional population-based study was carried out in a sample of 2,022 adults aged 20 to 59 years living in the urban area of a medium sized city in Southern Brazil. A questionnaire including socioeconomic, demographic, smoking, alcohol, and use of dental service variables was applied at adults household. Toothache occurred six months previous of the interview was considered the outcome. Poisson regression analyses were performed following a theoretical hierarchical framework. All analysis was adjusted by the sample design effect. Results: The response rate was 98.6%. The prevalence of toothache was 18.0% (95% CI 16.0; 20.1). The following variables were associated with toothache after adjustment: female (PR = 1.3 95% CI 1.3; 2.0), black skin colour vs. whites (PR = 1.5 95% CI 1.1, 1.9), low per capita income (PR = 1.7 95% CI 1.2, 2.3), smokers (PR = 1.5 95% CI 1.2, 1.9) and those who reported alcohol problems (PR = 1.4 95% CI 1.1; 1.9). To be 40 years of age (PR = 0.5 95% CI 0.4, 0.7) and use dental service in the last year (RR = 0.5 95% CI 0.4, 0.6) were protective factors for toothache. Conclusion: The prevalence of toothache in adults of Lages can be considered a major problem of dental public health.Mirian Kuhnen, Marco A Peres, Anelise V Masiero and Karen G Pere