Hopf bifurcation of an age-structured virus infection model (Q1671063)

The authors extend previous models to study the behavior of a viral infection with explicit cell infection-age structure, logistic target cell growth rate, and viral absorption by infected cells. For this purpose, the reproduction number as a threshold is obtained and the local stability of disease-free equilibrium and infection equilibrium are studied. A persistent analysis of the system shows the dependence on the basic reproduction number \(R_{0}\). Constructing a suitable Lyapunov function, the global stability of the uninfected equilibrium for \(R_{0}\leq1\) is established. Special cases showing Hopf bifurcations are studied, along with quantification of viral re-infection and recombination rates. An optimal reproduction number is determined and it is proved that the infection-free equilibrium is globally asymptotically stable. By choosing different parameters values the unique infection equilibrium can destabilize by means of a Hopf bifurcation. In this unstable case, the authors show sustained oscillations by numerical examples. However, there are some limitations to this study: although the model predicts clearance of the virus when \(R_{0}\leq1\), a current treatment for HIV cannot eradicate the virus due to latently infected cells, which are not, targeted by antiviral therapy.