Hepatitis B Virus With The Immune Response Time Delay Dynamics Model

Immune response to viral infection is common, which is a necessary pathway to eliminateand control the disease. Such as phagocytic cells, natural killer cells, interferon, antibodies,T cells And so on,which is the virus ordinary integral part of the immune response. In fact,in most of the cell infection by virus, cytotoxic T lymphocytes(CTL) by attacking the cellswhich is infected by virus, which plays a key role in virus defense. At the same time inthe process virus infection and the host body to produce immune response, just as after thehealthy cells are infected, the virus infected cell separation of free, the virus is cleared andthe body's immune defenses, such acts are established according to di?erent viruses havedi?erent time lags. In fact, because of these irregular time sequences existence, the patientsof immune status may produce certain e?ects. In mathematics show for periodic solutionor chaos. Virus dynamics in the study which was introduced when the immune responseand time delay will be better able to describe the corresponding spread of the virus and theimmune response and other dynamic features. Therefore this paper did a study for HBV.Paper is divided into three chapters.In the first chapter. Brief introduction to the dynamics of infectious diseases researchsignificance, domestic and international research profile of hepatitis B virus and the majorwork of this article.In the second chapter. Established a dynamic model of hepatitis B virus delay, consid-ered the CTL immune response to the infected cells. Proved that when the basic reproductivenumber is less than 1, the disease-free equilibrium is locally asymptotically stable. At thesame time, using the comparison theorem, disease-free equilibrium of the global asymptoticstability is proved. Obtained by the monotone iterative method for global stability of positiveequilibrium conditions. Illustrated by the numerical simulation of the main conclusions.In the three chapter. We study a class of lysis and non-lysis pathway of dynamic modelof hepatitis B virus. Study the basic properties of the model, and the equilibrium andstability conditions. Others, analysis the conditions of the model when the Hopf bifurcation happened. And the numerical simulation proves the chapter's main conclusion.