‎hepatitis b virus (hbv) infection is a major public health problem in the world today‎. ‎a mathematical model is formulated to describe the spread of hepatitis b‎, ‎which can be controlled by vaccination as well as treatment‎. ‎we study the dynamical behavior of the system with fixed control for both vaccination and treatment‎. ‎the results shows that the dynamics of the model is completely de...

In this paper, we studied a new kind of vector equilibrium problem, we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and KKM theorem these two tools,then we generalized this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds is a open problem proposed by Isac, Sehgal and Singh in 1999....

Consider a model of debt management, where sovereign state trades some bonds to service the with pool risk-neutral competitive foreign investors. At each time, government decides which fraction gross domestic product (GDP) should be used repay debt, and how much devaluate its currency. Both these operations have effect reduce actual size but social cost in terms welfare sustainability. When deb...