Dynamic Of HCV Infection Models With Antibody Immunity

Hepatitis C virus(HCV)is the main type of hepatitis viruses that cause chronic viral hepatitis.There are two modes of HCV infection,namely virus-to-cell infec-tion and cell-to-cell transmission,both of which can promote the production of the viruses.After the viruses invade the body,the immune system will carry out specific immunity against the viruses.Humoral immunity depends on the killing effect of antibodies to control viral replication.In this dissertation,we propose two mathematical models,one time-delay HCV infection dynamic model with antibody immunity,and the other two-strain HCV infection dynamic model with antibody immunity.The main contents are as follows:In chapter 2,a dynamic model of time-delay HCV infection with antibody immunity is established according to the mechanism of HCV infection.The model includes the virus-to-cell infection and cell-to-cell transmission.First of all,the existence,positivity and boundedness of the model solutions are proved,and the equilibria and threshold conditions of the model are calculated.Secondly,the local asymptotic stability of each equilibrium is proved,and then the global asymptotic stability of each equilibrium is proved by the approach of Lyapunov functionals.When R₀<1,the infection-free equilibrium E₀is globally asymptotically stable;when R₁<10,the immune-free equilibrium E₁is globally asymptotically stable;when R₂>1,the immune equilibrium E₂is globally asymptotically stable.In the end,the analytical results are illustrated by numerical simulations.In chapter 3,we consider a dynamic model of two-strain viruses with immune responses.Firstly,we prove the existence,nonnegativity and boundedness of solu-tions.Secondly,we define the basic regeneration number of the two virus strains,and obtain conditions on the existence of at most six equilibria(no-infection equi-librium,four boundary equilibria,and one coexistence equilibrium)in the model.Thirdly,we prove the stability of each equilibrium point.Finally,we use nu-merical simulations to illustrate and expand the analytical results.