Rumor is an important form of social interaction, and its spreading has a significant impact on people’s lives. In the age of Web, people are using electronic media more frequently than ever before, and blog has become one of the main online social interactions. Therefore, it is essential to...

When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge–Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and...

We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre manifold theory and techniques. Aspects of several...

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a...

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network and reveal the transmission parameters which govern the...

We present the stochastic differential equation with quenched noise for the Tang and Leschhorn model (Phys. Rev. A 45 (1992) R8309). The equation derived from the microscopic rules using regularization procedure predicts accurately the roughness, the dynamical and velocity exponents of the...

The analytical continuous equations for the Tang and Leschhorn (Phys. Rev. A 45 (1992) R8309) and the Buldyrev et al. (Phys. Rev. A 45 (1992) R8313) models are derived from the microscopic rules using a regularization procedure. As was shown in a previous paper (Phys. Rev. E 62 (2000) 6970) the...

For an epidemic model of the type mentioned, we prove a theorem on almost sure exponential stability of the disease-free equilibrium. For small values of the diffusion parameter, σ, we describe the stability of the disease free equilibrium point in terms of an appropriate analogue, Rσ, of the...