In this paper, we consider a stochastic SIS epidemic model with vaccination. We prove that the densities of the distributions of the solution can converge in L1 to an invariant density under appropriate conditions. Also we find the support of the invariant density.

A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak–Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into account business rule(s), like enterprise–enterprise...

The main purpose of the paper is to show that there exists intrinsically stochastic circular motion in a pairwise epidemic model, which does not exist in the classical mean-field susceptible–infective–susceptible (SIS) models. Here a basic pairwise SIS epidemic model is adopted. By the...

Physical modeling the dynamics of network growth help in the understanding of statistical properties of real networks. We describe here a statistical model supported on the random walk theory that generates several statistical connectivity properties observed in real networks. This formalism...

The travelling salesman problem, in which the best route between cities to be visited is chosen from a large number of possible routes, is reconsidered using the time reversal of physical dynamics, e.g. an inverse of the diffusion process. Information mediators assigned to every city diffuse as...

In this paper, the dynamical process of money creation in a random exchange model with debt is investigated. The money creation kinetics are analyzed by both the money-transfer matrix method and the diffusion method. From both approaches, we attain the same conclusion: the source of money...

We analyze, by means of the nonparametric estimation of the hazard function, the distribution of the earthquake occurrences in two regions of Spain. First, we present the method of estimation and the framework, and next we compare the seismic risk in the region of Galicia (northwest of Spain)...