Modeling The Co-infection Of HIV And Hepatitis B Virus In China

HIV(AIDS virus)and HBV(hepatitis B virus)are two major diseases that threaten human health.Because HIV and HBV infection pathways are very similar(e.g.,maternal,child,blood and sexual transmissions),there are about 4 million HIV-HBV co-infection cases in the world,Among the HIV infected persons,5%?15%were co-infected with HBV,and about 1%of HBV infected patients were infected with HIV,and the HIV-HBV co-infection rate was 14.6%before 2012 in China.To explore the mechanisms of the domestic HIV-HBV co-infection and search for control,we propose a differential equation model of HIV-HBV co-infection.First,we study the HBV-only model and the HIV-only model,evaluate separately the basic reproduction numbers R1 and R2,and discuss separately the local or global stability of the disease free equilibrium and endemic positive equilibrium;Secondly,we analyze the whole HIV-HBV co-infection model and calculated its basic regeneration number R0 = ?max{R1,R2},discuss the local or global stability of disease free equilibrium and two boundary equilibrium points,and prove that there is at least one positive endemic equilibrium by proving the uniform persistence of the diseases;then,we analyze the sensitivity and partial correlation of the basic reproductive number R0,find that the effective rate of HIV infection is the most important factor and the effective rate of hepatitis B infection is slightly less,and use the model to fit the China HIV data,also predict the situation of domestic co-infected patients;finally,based on the above research,we put forward the following measures to prevent and control HIV-HBV co-infection:increase the public's preventive measures on HIV and HBV,further strengthen the vaccination coverage against hepatitis B virus,and treat the confirmed HIV patients simultaneously with the combination treatment of hepatitis B drugs.