This paper addresses the spread of tuberculosis through one-strain and two-strain models. We first present a basic model that incorporates fast and slow progression, effective chemoprophylaxis and therapeutic treatment. The system exhibits the traditional behavior. We prove that if the basic reproduction ratio R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable on the no...

We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is s...

A stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators. If a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted, or equivalently, are infinitely fast, then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics. This result...

We show that a nonlinear locally uniformly asymptotically stable infinite-dimensional system is automatically locally input-to-state stable (LISS) provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs. Also we prove that LISS is equivalent to existence of a LISS Lyapunov function. We show by means of a counterexample that if this uniformity is not p...

We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically sta...

An SEI model with distributed delay is proposed where the transmission and the death rates depend on the age of infection. The basic reproduction number R0 is identified as a threshold quantity for the stability of equilibria. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out. On the contrary, ifR0 > 1, then a locally asymptotically stable e...

We propose a solution to the problem of achieving consensus of the state of multiple systems connected over a network (over a directed graph) in which communication events are triggered stochastically. Our solution consists of a protocol design that, using intermittent information obtained over the network, asymptotically drive the values of their states to agreement, with stability, globally a...

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 give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential inf...

The stability of the positive fixed points of a discrete-time mathematical model for populations consisting of wild and genetically altered mosquitos proposed by Jia Li [1] is considered in this paper. The model is studied for proportional and constant mating rates. Under certain conditions the model with proportional mating rate has two positive fixed points, one unstable and the other locally...