The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Vertical Bone Measurements From Cone Beam Computed Tomography Images Using Different Software Packages.

This article aimed at comparing the accuracy of linear measurement tools of different commercial software packages. Eight fully edentulous dry mandibles were selected for this study. Incisor, canine, premolar, first molar and second molar regions were selected. Cone beam computed tomography (CBCT) images were obtained with i-CAT Next Generation. Linear bone measurements were performed by one observer on the cross-sectional images using three different software packages: XoranCat®, OnDemand3D® and KDIS3D®, all able to assess DICOM images. In addition, 25% of the sample was reevaluated for the purpose of reproducibility. The mandibles were sectioned to obtain the gold standard for each region. Intraclass coefficients (ICC) were calculated to examine the agreement between the two periods of evaluation; the one-way analysis of variance performed with the post-hoc Dunnett test was used to compare each of the software-derived measurements with the gold standard. The ICC values were excellent for all software packages. The least difference between the software-derived measurements and the gold standard was obtained with the OnDemand3D and KDIS3D (-0.11 and -0.14 mm, respectively), and the greatest, with the XoranCAT (+0.25 mm). However, there was no statistical significant difference between the measurements obtained with the different software packages and the gold standard (p> 0.05). In conclusion, linear bone measurements were not influenced by the software package used to reconstruct the image from CBCT DICOM data.