This article concerns the SIRC epidemiological model for influenza A, which efficiently describes the mechanism of disease spreading, including the susceptible (S), the infected (I) and the recovered (R), along with a crossimmune class (C) that recovers after being inflected by different strains of the same viral subtype. The dynamics of the model is completely determined by the basic reproduct...

In this paper, we consider global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyap...

In this paper, we investigate the local and global stability and the period two solutions of all nonnegative solutions of the difference equation, xn+1 = axn + bxn−k A + Bxn−k where a, b, A, B are all positive real numbers, k ≥ 1 is a positive integer, and the initial conditions x−k, x−k+1, ..., x0 are nonnegative real numbers. It is shown that the zero equilibrium point is globally asymptotica...

A more realistic two-stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model are determined by...

This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instan...

ABSTRACT. For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically ...

In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number R0 of the model is obtained. We investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the infection-free equilibrium is globally asymptotically stable, whereas if R0 > 1, then the infection equilibrium is global...

In this paper we propose an age-structured malaria within-host model taking into account multi-strains interaction. We provide a global analysis of the model depending upon some threshold T0. When T0 ≤ 1, then the disease free equilibrium is globally asymptotically stable and the parasites are cleared. On the contrary if T0 > 1, the model exhibits the competition exclusion principle. Roughly sp...

Stability A globally asymptotically stable equilibrium is a state with the property that all solutions converge to this state, with no large excursions. Stabilization A system is stabilizable (with respect to a given state) if it is possible to find a feedback law that renders that state a globally asymptotically stable equilibrium. Lyapunov and control-Lyapunov functions A controlLyapunov func...

By incorporating an additional recovery compartment in the SLBS model, a new model, known as the SLBRS model, is proposed in this paper. The qualitative properties of this model are investigated. The result shows that the dynamic behavior of the model is determined by a threshold R0. Specially, virus-free equilibrium is globally asymptotically stable if R0 ≤ 1, whereas the viral equilibrium is ...