Mitsunobu Reactions Catalytic in Phosphine and a Fully Catalytic System

The Mitsunobu reaction is renowned for its mild reaction conditions and broad substrate tolerance, but has limited utility in process chemistry and industrial applications due to poor atom economy and the generation of stoichiometric phosphine oxide and hydrazine by‐products that complicate purification. A catalytic Mitsunobu reaction using innocuous reagents to recycle these by‐products would overcome both of these shortcomings. Herein we report a protocol that is catalytic in phosphine (1‐phenylphospholane) employing phenylsilane to recycle the catalyst. Integration of this phosphine catalytic cycle with Taniguchi’s azocarboxylate catalytic system provided the first fully catalytic Mitsunobu reaction.     

Modeling peer influence effects on the spread of high–risk alcohol consumption behavior

Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high–risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on alcohol addiction by assuming that susceptibles become heavy drinkers through the mechanism of imitation. We show that the model may exhibit the phenomenon of backward bifurcation. This means that alcohol problems may persist in the population even if the basic reproduction number is less than one. Nonlinear stability analysis of equilibria is also provided.     

Global stability for an HIV-1 infection model including an eclipse stage of infected cells

We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (2007) [37]. One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. In Rong et al. (2007) [37], the stability of the infected equilibrium has been analyzed locally. Here, we perform the global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on the higher-order generalization of Bendixson?s criterion. We obtain sufficient conditions written in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.     

Globally stable endemicity for infectious diseases with information-related changes in contact patterns

SIR and SIS epidemic models with information—related changes in contact patterns are introduced. The global stability analysis of the endemic equilibrium is performed by means of the Li–Muldowney geometric approach. Biological implications of the stability conditions are given.