Dynamical Analysis Of Two Classes Of Viral Infection Models With Age Structures And Nonmonotonic Immune Responses

The study of the dynamics of viral infection models is a hot topic in the field of biomathematics.By establishing an appropriate mathematical model and analyzing the dynamic properties of the model,the control threshold of related diseases can be identified,which is beneficial for the prevention and control of virus related diseases.This paper establishes two kinds of age-structured virus immune models based on the mechanism of viral infection and immune response,which are divided into the following two parts:Firstly,we consider the effector B cells in viral infection,which will produce antibodies by stimulated by the virus to neutralize with free virus.By assuming that the stimulus is nonmonotonic,we establish an age-structured viral infection model with nonmonotonic non-lytic immune response.The well-posedness of the model solution is studied,and by selecting appropriate thresholds,the existence and stability of the equilibria are analyzed,it is found that the system has bistable behavior,then the global stability of the equilibria is analyzed.And by selecting immune intensity as bifurcation parameter,saddle-node bifurcation and backward/forward bifurcation will occur.Finally,the results of theoretical analysis are verified through numerical simulation.Then we consider the non-lytic immune response in viral infection,some immune cells,stimulated by the virus,secrete cytokines to inhibit virus proliferation,rather than directly killing the virus.By assuming that the stimulus is also nonmonotonic,we establish an age-structured viral infection model with nonmonotonic non-lytic immune response.The well-posedness of the model solution is studied,and by selecting appropriate thresholds,the existence and stability of the equilibria are analyzed,it is found that the system also has bistable behavior,the global stability of the equilibrium is also analyzed.By selecting immune intensity as bifurcation parameter,saddle-node bifurcation and backward/forward bifurcation will also occur.Finally,the results of theoretical analysis are verified through numerical simulation.