Mathematical analysis of an influenza A epidemic model with discrete delay

Recently, a large number of mathematical models that are described by delay differential equations (DDEs) have appeared in the life sciences. In this paper, we present a delay differential model to describe influenza A (H1N1) dynamics. We begin by presenting the model with a brief discussion, followed by proving the positivity and boundedness of the model solution. We establish sufficient conditions for the global stability of the equilibria (the infection free equilibrium and the infected equilibrium), these conditions are obtained by means of the Lyapunov LaSalle invariance principle of the system. Also we have carried out bifurcation analysis along with an estimated length of delay to preserve the stability behavior. In particular, we show the threshold dynamics in the sense that if (reproduction number) R0<1 the infectious population disappear so the disease dies out, while if R0>1 the infectious population persist. Sensitivity analysis of the influenza A (H1N1) model reveals which parameter values have a major impact on the model dynamics. Numerical simulations with application to H1N1 infection are given to verify the analytical results.