Global Kinetic Analysis Of An HTLV-I Virus Infection Model With Age Structure

The establishment,of mathematical models has been widely used in many fields,especially in the study of infectious diseases and viral infections.In real life,the disease caused by virus infection has always affected human health.The establishment of mathematical model plays an important role in understanding this problem.Mathematical model research method is mainly through understanding the mechanism of virus infection,to establish the mathematical model of virus infection,and by studying the dynamic properties of the mathematical model of virus infection related,combining the biological significance of each variable in the model,to study the infection of internal mechanism of infection,which is applied to the prevention and control of infectious diseases.Considering that time delay is ubiquitous in the process of viral infection,many scholars use delay differential equations to describe the process of viral infection.Considering the time required for the activation of mature immune cells and the decay of immature immune cells in the process of virus infection,a class of age-structured HTLV-? virus infection model was established in this paper.Firstly,we proved the positive and uniformly bounded properties of the model solutions.And calculated the number of virus infection regeneration R0 and the number of immune regeneration RCTL,obtained the existence theorem of equilibrium point.By constructing Lya.punov functional and LaSalle invariant principle,the global stability of uninfected equilibrium point P0 and immune inactive equilibrium P1 is obtained.When R0<1,the uninfected equilibrium P0 is globally asymptotically stable;When RCTL<10,and can reach global asymptotically stable when some conditions are satisfied.When RCTL>1,the introduction of time delay changes the stability of the immune activation equilibrium P2.Furthermore,the stability of the immune activation equilibrium point,the existence of local Hopf bifurcation and the existence and boundedness of global Hopf bifurcation are analyzed by analyzing the distribution of the eigenroots of the characteristic equation,the central manifold theory,the normative theory and the global Hopf bifurcation theorem.