Mathematical Biosciences and Engineering (MBE)

Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection

Pages: 525 - 536, Volume 12, Issue 3, June 2015      doi:10.3934/mbe.2015.12.525

       Abstract        References        Full Text (441.0K)       Related Articles       

Yu Ji - Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China (email)

Abstract: In this paper, the dynamical behavior of a viral infection model with general incidence rate and two time delays is studied. By using the Lyapunov functional and LaSalle invariance principle, the global stabilities of the infection-free equilibrium and the endemic equilibrium are obtained. We obtain a threshold of the global stability for the uninfected equilibrium, which means the disease will be under control eventually. These results can be applied to a variety of viral infections of disease that would make it possible to devise optimal treatment strategies. Numerical simulations with application to HIV infection are given to verify the analytical results.

Keywords:  Time delay, stability, virus infection, general incidence rate, HIV.
Mathematics Subject Classification:  Primary: 34K20, 34K25; Secondary: 92D30.

Received: October 2014;      Accepted: December 2014;      Available Online: January 2015.