This paper considers a non-linear mathematical model for HIV epidemic that spreads in a variable size population through both horizontal and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 < ...

|In the present paper we provide an answer to the long-standing question of designing asymptotically stable proportional plus integral regulators with only position feedback for robots with uncertain payload. It has recently been shown in 1], 2] that globally asymptotically stable set-point regulators for robot manipulators without velocity measurement can be obtained replacing the velocity fee...

This paper deals with asymptotically controllable systems for which there exists no smooth stabilizing state feedback. To investigate the robustness asymptotic stabilization property, a new class of hybrid feedbacks (with a continuous component and a discrete one) is introduced: the hybrid patchy feedbacks. The notion of solutions is a generalization of π-solutions and Euler solutions. It is pr...

The spread of tuberculosis is studied through two models which include fast and slow progression to the infected class. For each model, Lyapunov functions are used to show that when the basic reproduction number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is globally asymptoti...

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and g...

We study a susceptible-infected-susceptible model with distributed delays. By constructing suitable Lyapunov functionals, we demonstrate that the global dynamics of this model is fully determined by the basic reproductive ratio R0. To be specific, we prove that if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. On the other hand, if R0>1, then the endemic equilibriu...

A model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differential equations. The model takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response. By constructing a block, the global stability of the uninfected steady state is investigated. This steady s...

In this paper, the global stability analysis of pertussis model with maternally derived immunity is studied. The qualitatively analysed to investigate asymptotic behavior respect equilibria. Using Lyapunov function method, pertussis-free equilibrium determined be globally asymptotically stable when associated basic reproduction number less than unity. Furthermore, study also extended prove exis...

The hybrid dynamics of the genetic regulatory networks (GRNs) have attracted much research attention in recent years. This paper is concerned with the stability analysis of piecewise GRNs. Depending on whether the state partitions and mode transitions are known or unknown as a priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, b...

A version of the global Galerkin method applied to a wide range of hydrodynamic stability problems is described. The numerical algorithm is based on a non-orthogonal set of globally defined basis functions, which satisfy all linear boundary conditions and the continuity equation. This leads to a significant reduction of the number of scalar degrees of freedom of the numerical model. The relativ...