Lyapunov function and global stability for a two-strain SEIR model with bilinear and non-monotone incidence

In this paper, we study a multi-strain SEIR epidemic model with both bilinear and non-monotone incidence functions. Under biologically motivated assumptions, we show that the model has two basic reproduction numbers that we noted [Formula: see text] and [Formula: see text]; and four equilibrium points. Using the Lyapunov method, we prove that if [Formula: see text] and [Formula: see text] are less than one then the disease-free equilibrium is Globally Asymptotically Stable, thus the disease will be eradicated. However, if one of the two basic reproduction numbers is greater than one, then the strain that persists is that with the larger basic reproduction number. And finally if both of the two basic reproduction numbers are equal or greater than one then the total endemic equilibrium is globally asymptotically stable. A numerical simulation is also presented to illustrate the influence of the psychological effect, of people to infection, on the spread of the disease in the population. This simulation can be used to determine the status of different diseases in a region using the corresponding data and infectious disease parameters.