Stability of discrete-time delayed influenza model with two-strain and two vaccinations

Abstract

This paper studies the global stability of a discrete-time delayed influenza model with two-strain and two vaccinations. We use nonstandard finite difference (NSFD) method to discretize the continuous-time influenza model. First we show that the solutions of the model are positive and bounded, then we calculate all possible steady states of the model. The model has four steady states; disease free steady state, two single-strain-infection steady states and a double-strain-infection steady state. The existence and stability of the steady states are governed by four threshold parameters. We investigate by utilizing Lyapunov approach, the global stability of the four steady states of the model. We provide numerical simulations to illustrate theoretical results. The effect of vaccination on influenza dynamics is discussed.