Biochemical genetics

The field under review is growing so rapidly that it is impossible to cover more than a sampling of recent papers in the allotted space. Important subjects such as the genetics and chemistry of viruses and certain topics in bacterial genetics have had to be omitted, while others have not received the treatment they deserve. Studies of a primarily biochemical nature in which mutants have been employed as tools have been reviewed, as is customary, although it is recognized that their genetic interest lies chiefly in their providing materials for the further study of gene action

Dynamical Behavior of a stochastic SIRS epidemic model

In this paper we study the Kernack - MacKendrick model under telegraph noise. The telegraph noise switches at random between two SIRS models. We give out conditions for the persistence of the disease and the stability of a disease free equilibrium. We show that the asymptotic behavior highly depends on the value of a threshold $\lambda$ which is calculated from the intensities of switching between environmental states, the total size of the population as well as the parameters of both SIRS systems. According to the value of $\lambda$, the system can globally tend towards an endemic case or a disease free case. The aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. Moreover, the attraction of the omega-limit set and the stationary distribution of solutions will be pointed out.Comment: 16 page