in this paper we study the dynamics of hepatitis b virus (hbv) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring  and also through contact with infective individuals. stability of the disease-free steady state is investigated. the basic reproductive rate, $r_0$, is derived. the results show that the dynamics of...

In this paper, we introduce a two-strain SIR epidemic model with viral mutation and vaccine administration. We discuss analyze the existence stability of equilibrium points. This has three types points, namely disease-free equilibrium, dominance point strain two, coexistence endemic point. The local two are verified by using Routh--Hurwitz criteria, while for global used suitable Lyapunov funct...

The paper describes an evolutionary game model of a P2P storage system. By studying the equilibrium point of the game, we demonstrate that an audit-based strategy, where audits are used to decide whether to cooperate with a given peer or not, may win or dominate free-riders peers that are using the system without contributing to it. This desirable equilibrium is reached for certain conditions a...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {it Bifurcation in...