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

Effects of the TVW on Knowledge Acquisition and Retention among Community Health Workers in Rwanda.

Effects of the TVW on Knowledge Acquisition and Retention among Community Health Workers in Rwanda.</p

Map of Nyamagabe district and the two targeted sectors (QGIS Ver. 3.28—CC-BY license 4.0.).

The layers are freely accessible from https://www.diva-gis.org/datadown and can be shared under CC-BY license 4.0.</p

Demographic profile of Community Health Workers that participated in the three VWT testing phases (N = 206).

Demographic profile of Community Health Workers that participated in the three VWT testing phases (N = 206).</p

Percentage of overall score obtained for the three evaluations done.

Percentage of overall score obtained for the three evaluations done.</p

Complete results from the assessment carried out with CHWs in southern Rwanda.

Assessments were carried out before the training (“Pre”), immediately after the training (“Post”) and 4 weeks later (“Follow-up”). (DOCX)</p

Interview Guide.

The pork tapeworm Taenia solium causes human taeniasis and cysticercosis when ingested as viable cysts and eggs, respectively. Despite its high health burden in low-income countries, knowledge of the parasite in endemic areas such as Rwanda is often limited. Here, we assess whether The Vicious Worm education software can increase knowledge in endemic areas of Rwanda. A cross-sectional mixed-methods study was conducted to evaluate knowledge about T. solium among community health workers trained using the Vicious Worm education software. Knowledge was assessed before, immediately after, and four weeks after the training. The health workers perceptions of the software were analysed thematically. A total of 207 community health workers were recruited from Nyamagabe district in Southern Province, Rwanda. Participants were composed of males (33.5%) and females (66.5%), aged between 22 and 68 years, and most (71%) had only completed primary education. Knowledge of cysticercosis at baseline was low, particularly knowledge of human cysticercosis and neurocysticercosis. The overall knowledge score increased significantly after training and was maintained four weeks after the training. Overall, insufficient knowledge was associated with neurocysticercosis-related questions, which after the training, remained relatively lower compared to questions of other categories. Participants reported the software to be user-friendly and educational. Digital illiteracy and the lack of smartphones were among the critical challenges highlighted in responses. This study has shown gaps in knowledge regarding T. solium infections within rural Rwanda, particularly neurocysticercosis. Health education using the Vicious Worm education software should be considered in integrated control programs.</div

Study Questionnaire Tool for the evaluation of knowledge about T. solium cysticercosis/Taeniasis.

Study Questionnaire Tool for the evaluation of knowledge about T. solium cysticercosis/Taeniasis.</p

The disease burden of congenital toxoplasmosis in Denmark, 2014

<div><p>Background</p><p>Congenital toxoplasmosis (CT) causes a substantial disease burden worldwide. The aim of this study was to estimate the disease burden of CT in Denmark, a developed country with free public healthcare and nationwide data available.</p><p>Methods</p><p>Using data primarily from two public health surveillance programmes conducted between 1992 and 2007, we estimated the incidence, occurrence of sequelae, mortality and the burden of disease in terms of disability-adjusted life years (DALYs) of CT in Denmark in 2014.</p><p>Findings</p><p>We estimated that 14 children were born with CT in 2014, of which six will have developed sequelae by the age of 12. CT resulted in a total disease burden of 123 DALYs (95% uncertainty interval [UI], 100–148), of which 78 (95% UI, 64–94) were due to foetal loss and 2 (95% UI, 1–3) were due to neonatal death; the remaining burden was due to moderate to severe life-long sequelae. A comparison of the estimated incidence of CT with the number of reported CT cases in 2008–2014 indicated that for each reported CT case, at least five other CT cases could be expected to have occurred and gone unreported.</p><p>Interpretation</p><p>Early onset, severity, and life-long duration of sequelae have a major effect on the disease burden of CT. Our data suggest that CT is under-diagnosed or under-reported in Denmark. The estimated disease burden and public health impact in Denmark is lower than in other European countries, highlighting the need for country-specific studies.</p></div

Parameters used to estimate the incidence of congenital toxoplasmosis (CT) and selected associated health outcomes.

<p>Parameters used to estimate the incidence of congenital toxoplasmosis (CT) and selected associated health outcomes.</p