Dynamics Of A Delay Epidemic Model With CTL Immune Response

Most virus can not go directly into cells, but immune antibody composition in thebody cannot enter into cells directly to kill virus when the body is suffered from virusinfection. Base on the fact that antigenic stimulation will generate Cytotoxic TLymphocytes that it is short for CTLs. The existing activate CTL cells make the targetcells death, cracking and it also make the virus component exposed. At last, theantibodies in the humoral immune components completing immune response is to killthe virus.Base on human body’s immune response system that the virus infectious modelwith CTL immune reaction is studied in this paper. Taking into account the body’shealthy cells from virus infection stimulation to become infected cells needs a certainamount of time. Based on the fact that a latent period between antigenic stimulation andgenerating CTLs, constant delay is introduced in the systems, we set up the viralinfection model with immune response and study the property of this model.In this paper we consider a delayed CTL pathogenesis model under the classicalCTL model and study the following content by taking as the parameter:Firstly, it is mainly proved that the solutions of system are positive and ultimatelyuniform bounded by using contradiction;Secondly, by analyzing the basic reproduction ratio for viral infection and CTLimmune response, the existence of three equilibria is established. We propose that theequilibrium point is locally asymptotically stable by applying Routh-Hurwitz criterion.By means of suitable Lyapunov functions and LaSalle’s invariant principle, we discussthe global stability of the infection-free equilibrium, the CTL-inactivated infectionequilibrium, and the CTL-activated infection equilibrium. We also carry out somenumerical examples to illustrate the the theoretical results, and for comparison withprevious conclusions, indicating the superiority of this paper has concluded;Thirdly, we use Simulink package in Matlab to do numerical simulations to supportour theoretical analysis and prove the correctness of the theory that we obtain.