This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or contractive self-mappings from initial c...

We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptoticall...

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon If the basic reproduction number R is below unity the disease free equilibrium P is globally stable in the feasible region and the disease always dies out If R a unique endemic equilibrium P is globally asymptotically stable in the interior of the feasible regi...

The conjecture of Arino and van den Driessche (2003) that a SIS type model in a moverstayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative or...

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number R0 are identified and its threshold properties are discussed. When R0<1, the infection-free equilibrium E0 is globally asymptotic...

The global stability for a delayed HBV infection model with CTL immune response is investigated. We show that the global dynamics is determined by two sharp thresholds, basic reproduction number <0 and CTL immune-response reproduction number <1. When <0 ≤ 1, the infection-free equilibrium is globally asymptotically stable, which means that the viruses are cleared and immune is not active; when ...

In this paper, we rigorously analyse an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus. We show that when the basic reproduction ratio ℛ(0)<1, then the infection-free equilibrium E (0) is globally asymptotically stable; when ℛ(0)>1, E (0) loses its stability and there is the single-infection equilibrium E (s). If ℛ(0)∈(1, 1+δ) where ...

In this paper, an HIV infection model including an eclipse stage of infected cells is considered. Some quicker cells in this stage become productively infected cells, a portion of these cells are reverted to the uninfected class, and others will be latent down in the body. We consider CTL-response delay in this model and analyze the effect of time delay on stability of equilibrium. It is shown ...

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/driveresponse systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Non...

We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will consider chemical reaction systems that are weakly reversible, have a deficiency of zero, and are equipped with mass action kinetics. We show that if for ...