The Research On Two Types Of Virus Infection Model With Humoral Immunity

For the past,few years,virus infectious diseases have attracted extensive attention at home and abroad.This paper has mainly investigated two types of virus infection model with humoral immunity.The main contents and frame of the article is as follows:1.In the first,part(section 2),a reaction-diffusion virus infection model with hu-moral immunity and nonlinear incidence is proposed.In spatially heterogeneous case,the basic reproduction number of virus infection R0 is calculated,when R0?1 the global asymptotical stability of the infection-free steady state is established,and when Ro>1 the uniform persistence of infected cells and viruses,as well as the existence of antibody-free infection steady state are also obtained.In spatially homogeneous case,the antibody response basic reproduction number R1 is calculated,by using the Lyapunov functions method and the persistence theory of dynamical systems we obta.in that,when R0>1 and R1?1 the antibody-free infection equilibrium is globally asymptotically stable,and when R0>1 and R1>1 the model is uniformly persistent and the infection equilibrium exists and is also globally asymptotically stable.Finally,the numerical examples are presented in order to verify the validity of our theoretical results and the rationality of our conjectures.2.In the second part(section 3),a infectious disease model with humoral immunity coupling within-and between-host dynamics is proposed.By using the methods of limiting system,we separate the model into the fast subsystem within-host and the slow subsystem between-host.For the fast system,we obtain the existence of equilibriums and establish the threshold conditions of global stabilities of equilibriums by using the method of Lyapunov functions.For the slow system,when antibodies in host don't react,we obtain that there may exist a backward bifurcation.However,when antibodies in host react,we establish the threshold conditions of global stabilities of equilibriums.Therefore,antibodies in host play an important role in controlling the spread of disease.Specifically,when the density of antibodies in host reach acertain level,the disease between hosts will stamp out.Finally,the numerical examples are presented to verify the validity of the theoretical results.