This paper studies how amatching rule affects the evolution of fairness in the ultimatumgame. Gale et al. [1995] show that under the randommatching rule, a partially fair imperfect Nash equilibrium in which all proposers are fair but some responders are selfish is asymptotically stable in the limit as noise in learning vanishes if responders are noisier than proposers. This paper shows that, un...

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...

We present a simple general method for estimating the thickness of heavy tails based on the asymptotics of the sum. The method works for dependent data, and only requires that the centered and normalized partial sums are stochastically compact. For data in the domain of attraction of a stable law our estimator is asymptotically log stable, consistent and asymptotically unbiased, and converges i...

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...

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 ...

We consider a reaction-diffusion equation in one space dimension whose initial condition is approximately a sequence of widely separated traveling waves with increasing velocity, each of which is asymptotically stable. As in [25], [24], and [14], we show that the sequence of traveling waves is itself asymptotically stable: as t → ∞, the solution approaches the concatenated wave pattern, with di...

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 the present paper, the modified Runge-Kutta method is constructed, and it is proved that the modified Runge-Kutta method preserves the order of accuracy of the original one. The necessary and sufficient conditions under which the modified Runge-Kutta methods with the variable mesh are asymptotically stable are given. As a result, the θ-methods with 1 2 ≤ θ ≤ 1, the odd stage Gauss-Legendre m...

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...