Center manifold analysis and Hopf bifurcation of within-host virus model

Document Type : Research Paper


1 Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16315-1618, Tehran, Iran

2 Department of Mathematics, University of Garmsar, P. O. Box: 3581755796, Garmsar, Iran

3 Department of Virology, School of Medicine, Iran University of Medical Sciences, Tehran, Iran


A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there exists a unique infectious equilibrium which may or may not be stable. In the case of instability, there exists an asymptotically stable periodic solution. Secondly, an analysis of local center manifold shows that when R0 = 1, a transcritical bifurcation occurs where upon increasing R0 greater than one the DFE loses stability
and a locally asymptotically positive infection equilibrium appears.