Global dynamics of an SEIQR model with saturation incidence rate and hybrid strategies

An SEIQR epidemic model with the saturation incidence rate and hybrid strategies was proposed, and the stability of the model was analyzed theoretically and numerically. Firstly, the basic reproduction number R₀ was derived, which determines whether the disease was extinct or not. Secondly, through LaSalle's invariance principle, it was proved that the disease-free equilibrium is globally asymptotically stable and the disease generally dies out when R₀<1. By Routh-Hurwitz criterion theory, it was proved that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R₀>1. Thirdly, according to the periodic orbit stability theory and the second additive compound matrix, it was proved that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R₀>1. Finally, some numerical simulations were carried out to illustrate the results.