A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium ap...

We study the SIR epidemic model with varying total population size and constant immigration rate. We derive the sufficient conditions on parameters of the system to guarantee that the equilibrium points of the system are locally asymptotically stable or globally asymptotically stable. If the disease-free equilibrium point is stable, then the disease will not affect the population in the system....

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibriu...

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also ...

The aim of this paper is to study the local stability of discrete epidemic models with specific nonlinear incidence rate. So, we establish criteria on local stability of the disease-free equilibrium, furthermore, using Schur-Cohn Criterion, important criterion on local stability of endemic equilibrium is also determined.

In this paper, we analyze a mathematical model of tuberculosis (TB) epidemics for stability with respect to the basic reproduction number Ro. The basic reproduction number Ro is determined. We give criteria for stability of the disease – free equilibrium (DFE) and the endemic equilibrium

A coepidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). The density of individuals infected with latent tuberculosis is structured by age since latency. The host population is divided into five subclasses of susceptibles, latent TB, active TB (wit...

We investigate the oscillatory reaction dynamics in a closed isothermal chemical system: the reversible Lotka-Volterra model. The second law of thermodynamics dictates that the system ultimately reaches an equilibrium. Quasistationary oscillations are analyzed while the free energy of the system serves as a global Lyapunov function of the dissipative dynamics. A natural distinction between regi...

A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with a proper definition of the cluster boundary. Here we demonstrate a shape-free determination of the free energy for temperature-driven cluster formation in pa...

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a sy...