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.

Preference Mapping Of Dulce De Leche Commercialized In Brazilian Markets.

Dulce de leche samples available in the Brazilian market were submitted to sensory profiling by quantitative descriptive analysis and acceptance test, as well sensory evaluation using the just-about-right scale and purchase intent. External preference mapping and the ideal sensory characteristics of dulce de leche were determined. The results were also evaluated by principal component analysis, hierarchical cluster analysis, partial least squares regression, artificial neural networks, and logistic regression. Overall, significant product acceptance was related to intermediate scores of the sensory attributes in the descriptive test, and this trend was observed even after consumer segmentation. The results obtained by sensometric techniques showed that optimizing an ideal dulce de leche from the sensory standpoint is a multidimensional process, with necessary adjustments on the appearance, aroma, taste, and texture attributes of the product for better consumer acceptance and purchase. The optimum dulce de leche was characterized by high scores for the attributes sweet taste, caramel taste, brightness, color, and caramel aroma in accordance with the preference mapping findings. In industrial terms, this means changing the parameters used in the thermal treatment and quantitative changes in the ingredients used in formulations.