Chemo-, Regio- And Stereoselective Heck Arylation Of Allylated Malonates: Mechanistic Insights By Esi-ms And Synthetic Application Toward 5-arylmethyl-γ-lactones.

We describe herein a general method for the controlled Heck arylation of allylated malonates. Both electron-rich and electron-poor aryldiazonium salts were readily employed as the aryl-transfer agents in good yields and in high chemo-, regio-, and stereoselectivity without formation of decarboxylated byproducts. Reaction monitoring via ESI-MS was used to support the formation of chelated Pd species through the catalytic cycle. Additionally, some Heck adducts were successfully used in the total synthesis of pharmacologically active γ-lactones.

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.