Global Dynamics Of A Virus Infection Model With Repulsive Effect

The paper is devoted to investigate the globally asymptotical stability of infection-free steady state,the existence and the persistence of positive non-constant steady states,the local and global structure of steady states and the criterion of stability for bifurcation solution for a virus infection model with repulsive effect.The paper has five chapters as follows:In the first chapter,we briefly introduce the background and significance of this work,the mathematical symbols used throughout this paper and the preliminary knowledge.In the second chapter,we prove that the system has a global attractor and a unique infection-free steady state,analyze the properties of the basic reproduction number R0,and establish the relationship between the basic reproduction number and the eigenvalues of the system linearized at the infection-free steady state by using the dynamical theory.In the third chapter,we use the Amann theory to prove that the system satisfies the comparison principle firstly.Then,the influence of the basic reproduction num-ber on the dynamic properties of the system is analyzed.We obtain that when the infection-free steady state is globally asymptotically stable,the condition R0?(?)is required,where (?)= maxx??T*(x),(?) = maxx???(x)and (?) = maxx???(x).If the system has a positive non-constant and uniformly persistent steady state,the R0? maxx??(?)is needed.Further,as corollaries,we conclude the relevant results on the corresponding system with constant coefficients.In the fourth chapter,we make the constant coefficient system dimensionless and treat diffusion coefficient of virus particles as a bifurcation parameter.By using the local and global bifurcation theory,we obtain the local and global structures of the non-constant steady states.The asymptotic expressions of the non-constant steady state is derived by using asymptotic analysis.The the stability criterion of non-constant steady state is established.Numerical results are agreement with the obtained theoretical results.In the fifth chapter,we summarize the main work of this paper,illustrate the innovation of this paper and put forward the work that can be further studied.