Analisis On A Class Of Delayed Virus Dynamics Model With Stage-structure

The bifurcation problem has always been one of the most important researchdirections in dynamical system. In the field of mathematical biology, by analyzingthe stability of equilibrium point and the existence of Hopf bifurcation, we canpredict orbits of the system being studied under different parameter conditions.Thus, provide us guidance to prevent and control wide-spreading of some kinds ofdiseases. In this paper, what we studied is a molecular-level dynamic in-hostsystem mainly about virus. It works in many kinds of diseases, say HIV andHepatitis B and so on. What’s more, the conclusions also provide valuable datawhich would work in clinic as reference.The paper first introduces the background knowledge of the viral dynamicmodel and the status quo of the research. Then the viral dynamics model isimproved based on the classic one. By adding the Holling structure to describe theeffect of mutual exclusion between viruses, we are closer to the mechanism ofviral infection among human cells. Taking advantage of distribution of the roots ofpositive equilibrium point’s characteristic equation in the following, the paperanalyzes the stability of the positive equilibrium point and gives a sufficientcondition for the existence of local Hopf bifurcation. The joint of central manifoldtheory and normal form method give us several equations to calculate importantparameters which can determine the properties of Hopf bifurcation. In the end ofthe paper, use Matlab to simulate in order to support the preceding theoreticalanalysis.