Study On The Dynamics Model Of Hepatitis B Virus With Drug-Resistant Treatment

Viral hepatitis B is a liver disease caused by a virus infection,which is called hepatitis B for short.Hepatitis B is one of the major infectious diseases under control in China.At present,antiviral treatment and vaccination are important means to control the hepatitis B epidemic.The main works of this paper are as followsFirstly,aiming at the problem that the mutation of hepatitis B virus reduces the effectiveness of drug-resistant treatment,a model of hepatitis B virus with drugresistant treatment is constructed,and the conditions for the existence of four equilibrium points in the model are given.The global asymptotic stability of all kinds of equilibrium points is proved by using Lyapunov function and the compound matrix method.The effect of drug resistance caused by viral mutation on drug treatment is simulated.It is found that the drug efficacy decreases with the increase of mutation rate.However,regardless of the mutation rate,the continuous usage of drugs can reach below the clinical treatment standard,but stopping treatment will cause the virus to rebound.Secondly,considering that the process of hepatitis B virus transmission is affected by random factors,a model of hepatitis B virus with random interference infection rate is established.By constructing Lyapunov function and using Ito's formula,it is proved that the stochastic hepatitis B model has unique global positive solution.The sufficient conditions for the asymptotic behavior of solution are given.The relationship between noise intensity and oscillation amplitude is obtained.The effects of noise intensity on the asymptotic behavior of the model and antiviral therapy are simulated,and the conclusion of the theorem is verified.It is also found that with the increase of mutation rate,the noise intensity will increase and the number of drug-resistant viruses will decrease.Therefore,the accurate monitoring of HBV DNA quantity will also be affected.Finally,in view of the problem that nucleoside drug resistance interferes with effective treatment,the mechanism of interferon's action on hepatitis B virus is considered,and a dynamic model of hepatitis B virus with nucleoside drugs and interferon combined therapy is established.The conditions for the existence of equilibrium point are given.By constructing Lyapunov function,the global asymptotic stability of the equilibrium point is proved.The change trend of the virus after the treatment of interferon and entecavir alone and the combination of two drugs under different mutation rates is simulated,and the reasonable treatment scheme is proposed according to different mutation rates.