A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants of integration in their results. An elimination of constants of integration opens the door to an operator that reconciles all known fractional derivatives and shows surprising results in areas unobserved before, including the appearance of the Riemann Zeta Function and fractional Laplace and Fourier Transforms. A new class of functions, known as Zero Functions and closely related to the Dirac Delta Function, are necessary for one to perform elementary operations of functions without using constants. The operator also allows for a generalization of the Volterra integral equation, and provides a method of solving for Riemann's "complimentary" function introduced during his research on fractional derivatives

Additional file 1: of The impact of individual-level heterogeneity on estimated infectious disease burden: a simulation study

Sensitivity analyses. (DOCX 86 kb

Additional file 1: of Zooprophylaxis as a control strategy for malaria caused by the vector Anopheles arabiensis (Diptera: Culicidae): a systematic review

Multilingual abstract in the six official working languages of the United Nations. (PDF 609 kb

Additional file 1:Table S1. of Mapping occurrence of Taenia solium taeniosis/cysticercosis and areas at risk of porcine cysticercosis in Central America and the Caribbean basin

Countries, territories, and institute contacts. (XLSX 11 kb

Additional file 2: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

List of references for the records included in the review. (XLSX 20 kb

Overview of the risk factors, with respectively regression coefficient and significance level of the univariable relations with seroprevalence, estimated with generalized linear models (1) and median and 95% credible interval (between squared brackets) of the multivariable relations with seroprevalence, estimated with Bayesian generalized linear regression (2<i>)</i>.

Overview of the risk factors, with respectively regression coefficient and significance level of the univariable relations with seroprevalence, estimated with generalized linear models (1) and median and 95% credible interval (between squared brackets) of the multivariable relations with seroprevalence, estimated with Bayesian generalized linear regression (2).</p

Graphical presentation of the random forest modeling showing the relative importance of the risk factors in relation to seroprevalence (using IncNodePurity).

Graphical presentation of the random forest modeling showing the relative importance of the risk factors in relation to seroprevalence (using IncNodePurity).</p

Additional file 3: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

Prevalence data extracted from the included records. (DOCX 98 kb

Additional file 1: of Epidemiology, impact and control of bovine cysticercosis in Europe: a systematic review

PRISMA 2009 Checklist. (DOC 65 kb

Nursing home specific questionnaire.

In a previous study in Belgian nursing homes (NH) during the first wave of the COVID-19 pandemic, we found a SARS-CoV-2 seroprevalence of 17% with a large variability (0–45%) between NH. The current exploratory study aimed to identify nursing home-specific risk factors for high SARS-CoV-2 seroprevalence. Between October 19th, 2020 and November 13th, 2020, during the second COVID-19 wave in Belgium, capillary blood was collected on dried blood spots from 60 residents and staff in each of the 20 participating NH in Flanders and Brussels. The presence of SARS-CoV-2-specific IgG antibodies was assessed by ELISA. Risk factors were evaluated using a questionnaire, filled in by the director or manager of the NH. Assessed risk factors comprised community-related factors, resident-related factors, management and performance features as well as building-related aspects. The relation between risk factors and seroprevalence was assessed by applying random forest modelling, generalized linear models and Bayesian linear regression. The present analyses showed that the prevalence of residents with dementia, the scarcity of personal protective equipment (surgical masks, FFP2 masks, glasses and face shields), and inadequate PCR test capacity were related to a higher seroprevalence. Generally, our study put forward that the various aspects of infection prevention in NH require more attention and investment. This exploratory study suggests that the ratio of residents with dementia, the availability of test capacity and personal protective equipment may have played a role in the SARS-CoV-2 seroprevalence of NH, after the first wave. It underscores the importance of the availability of PPE and education in infection prevention. Moreover, investments may also yield benefits in the prevention of other respiratory infections (such as influenza).</div