2,312 publications from this institution
Epidemiological models with bilinear incidence rate usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable nontrivial equilibrium (i.e.interior equilibrium) corresponding to the endemic state.In this paper, we consider an epidemiological model, which is a SIRS (susceptible-infected-removed-susceptible) model influenced by random perturbations.We prove that the solutions of the system are positive for all positive initial conditions and that the solutions are global, that is, there is no finite explosion time.We present necessary and sufficient condition for the almost sure asymptotic stability of the steady state of the stochastic system.
We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also evaluate the smallest eigenvalue and show that its reciprocal is approximately equal to the mean trapping time. We expect that our technique can also be adapted to other regular fractals with treelike structures.
