Mathematical Model Of Hepatitis B And Its Qualitative Analysis

Three types of hepatitis B virus mathematical model are discussed, a sufficientcondition for stability of equilibrium is obtained.firstly, a model for HBV infection with delay CTL-immune response isconsidered. The equilibrium points of system are found and their stability isinvestigated. A Lvapunov function is constructed，according to the relevant theory ofstability. It is proved that the model is globally stable at the disease elimination point.Besides, the stability switches occur and equilibrium is unstable as passes througha critical value. Numerical simulations are carried out to illustrate the obtained results.Secondly, Aimed at the shortcomings of the Revilla and Levins’s models, amodified cellular model by the drug treatment is proposed, which had predicted thelong-term effect for chronic HBV infection of drug treatment. the simulation resultsshow that the number of viruses is gradually stability in the use of drugs after threemonths. If the treatment is continual, the HBV may be entirely clear. If we choose thedifferent parameters, lots of differentiated ways of treatment might get.Finally, Tries to develop a mathematical model to express how the hepatitis Bvirus spreads over and transforms from a state into other one by a set of differentialequations. according to the relevant theory of stability, it is proved that the model islocally stable at the disease elimination point, It is a good advice that the disease orthe model should be controlled effectively by way of immunization，i．e，，isolatinginfants from their mothers and immunizing all infants.Guangju Wang (Applied Mathematics)Directed by Xinyuan Liao...