A Dynamical Model For Controlling HBV Transmission With Active Immunization And Drug Therapy

Hepatitis B(referred to as HB)is an infectious disease caused by hepatitis B virus.We usually take active immunization(vaccination)to prevent hepatitis B virus infection and take drug therapy to inhibit hepatitis B virus infection in vivo replication,thus controlling the spread of hepatitis B virus.Considering the requirement for clinical treatment of the disease,a pharmacokinetic model of multiple administration was established to analyze the regimen.The blood concentration-time relationship of different drug doses in two different administration modes was given.The results of the model were applied to the apnea treatment cases of premature infants,and the feasibility of the drug delivery scheme was analyzed in terms of safety,not waste and stable efficacy.According to the treatment of severe children,personalized drug therapy strategy was designed.Considering the influence of hepatitis B virus infection mainly from neonatal and immune failure factors,a SEICR model with active immune control for hepatitis B virus transmission was established.The sufficient conditions for the existence and global asymptotic stability of disease-free equilibrium and endemic equilibrium are given by using the theory of differential equations.Then,the numerical simulation verifies the rationality of the results.The results of numerical simulation show that active immunization is an effective way to control the spread of hepatitis B virus.Considering the effect of drug treatment on the control of HBV infection,the drug therapy rate of HBV infected patients was treated as a function of time during treatment,and the model of hepatitis B virus transmission dynamics with drug therapy was given.On this basis,in order to reduce the number of HBV infection,the objective function with a hepatitis B virus infection and drug treatment ratio is established.We use the existence conditions of the optimal control to prove the existence of the optimal proportion of treatment.The optimal drug therapy proportional expression was obtained by Pontryagin maximum.The feasibility of theresults was verified by numerical simulation.The results show that the proportion of patients with HBV infection decreased to 1% within 20 years when the proportion of optimal drug therapy is selected.