Study On The Stability Of Two Kinds Of Biological Models

This paper is divided into two sections.Firstly,we will study the global stability for a dynamic model of Hepatitis B with antivirus treatment. By applying a comparison theorem and analyzing the corresponding characteristic equations, it is proved that if the basic production number R0<1,the disease-free equilibrium is globally asymptotically stable.Furthermore, by using Lyapunov stability theorem and a geometrical approach, we obtain the global stability of the endemic equilibrium if R0>1, and the disease is uniformly permanent.Secondly,we will deal with the existence and nonlinear stability of large-amplitude traveling waves to a system of conservation laws arising in biology. By a delicate phase plane analysis and the method of energy estimates, we obtain sufficient conditions on parameters for the existence and asymptotic nonlinear stability of traveling wave solutions.