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

Finite pure bending of curved pipes

We present an original treatment for the finite bending of curved pipes with arbitrary cross sections. The curved pipe is successively regarded as a three-dimensional continuum and a shell, and a formulation is proposed for each model. We show that, from a numerical point of view, the finite bending problem is reducible to an axisymmetric analysis augmented with 1 d.f. We also show how to take advantage of this analogy to solve the bending problem using standard axisymmetric FE routine