Stability Analysis Of Delayed HTLV-Ⅰ Infection Model With CTL Immune Response And Immune Impairment

Human T-cell leukemia virus I(HTLV-Ⅰ)is the first retrovirus to be found to be associated with human disease.It can cause adult T-cell lymphocyte leukemia.At present,the pathogenesis of HTLV-Ⅰ is not clear,and there is no effective treatment method.Hence,the analysis of relevant mathematical models is helpful to understand the pathogenesis of HTLV-Ⅰ-related diseases,therefore,it is of great significance for the formulation of therapeutic measures.In the first chapter,we introduce the relevant knowledge of HTLV-Ⅰ infection,the investigative situation of HTLV-Ⅰ infection model,and then put forward the main research contents of this paper.In the second chapter,we consider a delayed HTLV-Ⅰ infection model with BeddingtonDe Angelis incidence,CTL immune response and immune impairment,including two kinds of delays: intracellular delay and CTL immune response delay.By calculation,the basic reproduction number and the existence of chronic infection equilibrium can be obtained.By analyzing the distribution of roots of characteristic equations,we can obtain the local asymptotic stabilities of equilibria and the existence of Hopf bifurcation.By constructing suitable Lyapunov functional and using La Salle’s invariance principle,the global threshold dynamics of the model is proved: if the basic reproduction number is less than unity,the infection-free equilibrium is globally asymptotically stable;if the basic reproduction number is greater than unity and immune response delay is equal to zero,the chronic-infection equilibrium is globally asymptotically stable.Finally,numerical simulation is carried out to illustrate theoretical results,and the correlation between parameters and reproduction number is explained by sensitivity analysis.In the third chapter,we consider a delay HTLV-Ⅰ infection model with nonlinear incidence,mitotic division,lytic and nonlytic immune responses and immune impairment.By computation,we obtain the basic reproduction number and the existence of chronicinfection equilibrium.By analyzing the distributions of roots of corresponding characteristic equations,it’s shown that the local stabilities of equilibria.Meanwhile,we discuss the existence of Hopf bifurcation and further study the direction of Hopf bifurcation and the stability of periodic solutions by using the normal form and the center manifold theory.By constructing suitable Lyapunov functional and using La Salle’s invariance principle,the global threshold dynamics of the model is proved: if the basic reproduction number is less than unity,the infection-free equilibrium is globally asymptotically stable;if the basic reproduction number is greater than unity and immune response delay is equal to zero,the chronic-infection equilibrium is globally asymptotically stable.Finally,numerical simulation is used to illustrate theoretical results.In the forth chapter,we summarize and prospect the research contents of this paper.