Based on the model provided by the Mulone and Straughan [1], we relax the population which are constant and obtain the drug-free equilibrium which is global asymptotically stable under some conditions. The system has only uniqueness positive endemic equilibrium which is globally asymptotically stable by using the second compound matrix.

Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can no...

This paper deals with the modeling of the strategic allocation of greenhouse gases emission allowances in the EU-wide trading market that results from Kyoto agreement implementation. An M -matrix game is formulated where the players are countries or groups of countries that may have a strategic influence through their allocation of emission allowances and the payoffs are the welfare gains of th...

Traffic flow can be understood as a realization of a broad class of one dimensional physical systems, where a hard core repulsive interaction competes with a longer ranged attraction between the particles. It can be shown rigorously that the statistical properties of such systems in thermal equilibrium are well described by a family of distributions that stems from the random matrix theory. Ana...

This paper provides a sufficient condition for the existence and uniqueness of a BayesianNash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobianmatrix of the payoff gradient is negative definite...

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow us to calculate the fluctuations and large deviations of the density and the current in non-equilibrium steady states of systems like exclusion processes. The...

Time-dependent matrix product states (time-dependent DMRG) has developed into a very powerful tool for the simulation of the evolution of strongly correlated quantum systems far from equilibrium. However, its scope is limited by the effective restriction to onedimensional systems as well as to relatively short times due to dynamical entanglement growth. In this talk, I want to show how a combin...

The advent of relativistic heavy-ion collision experiments as well as rapid progress in cosmological observations triggered an enormous increase of interest in the dynamics of quantum fields out of equilibrium. Much progress has been achieved for systems close to thermal equilibrium using (non-)linear response techniques or with effective descriptions based on a separation of scales in the weak...

The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model. The globally asymptotic stability of ...