Research On Periodicity Of HBV Infection

In this paper, the dynamic behavior of three HBV infection systems is studied. Applying impulsive differential equation theory,impulsive delay differential equation theory and coincidence degree theorem,the periodicity and stability of HBV infection systems are analyzed, Our results provide theoretical basis for the development, prediction and treatment of the hepatitis B disease. The main work is as follows:The HBV infection system with impulsive drug treatment effects is studied. By using the Floquet theory,we obtain conditions which guarantee the globally asymptotical stability of periodic solutions. Therefore, by taking appropriate treatment, the rate of replication of the virus can be suppressed and eventually cleared by drugs, then the state of the disease can be controlled.The HBV infection model with delay and impulsive medication is discussed. By use of impulsive differential equation comparison theorem, a condition for the existence and stability of periodic solutions is given, and the system’s persistence is also proved.The HBV infection model with immune response is studied. We proved that the system has at least one positive periodic solution by using the coincidence degree theory. This is a good explanation of the phenomenon of the patient’s body viral load fluctuations.