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.

Sim-xl: A Powerful And User-friendly Tool For Peptide Cross-linking Analysis.

Chemical cross-linking has emerged as a powerful approach for the structural characterization of proteins and protein complexes. However, the correct identification of covalently linked (cross-linked or XL) peptides analyzed by tandem mass spectrometry is still an open challenge. Here we present SIM-XL, a software tool that can analyze data generated through commonly used cross-linkers (e.g., BS3/DSS). Our software introduces a new paradigm for search-space reduction, which ultimately accounts for its increase in speed and sensitivity. Moreover, our search engine is the first to capitalize on reporter ions for selecting tandem mass spectra derived from cross-linked peptides. It also makes available a 2D interaction map and a spectrum-annotation tool unmatched by any of its kind. We show SIM-XL to be more sensitive and faster than a competing tool when analyzing a data set obtained from the human HSP90. The software is freely available for academic use at http://patternlabforproteomics.org/sim-xl. A video demonstrating the tool is available at http://patternlabforproteomics.org/sim-xl/video. SIM-XL is the first tool to support XL data in the mzIdentML format; all data are thus available from the ProteomeXchange consortium (identifier PXD001677).