Dynamic analysis of an SIQR model with saturation contact rate and hybrid strategies

Considering vaccination, quarantine and elimination hybrid strategies, an SIQR epidemic model with saturation contact rate was established. And the global stability of the model was studied by means of both theoretical and numerical ways. Firstly, the threshold-basic reproductive number R0 which determines whether the disease is extinct or not and the conditions for the existence of equilibriums were obtained by the calculation. Secondly, by Liapunov function, it was proved that the disease-free equilibrium P0 is globally asymptotically stable when R0<1. Thirdly, by constructing a suitable Dulac function, it was obtained that the unique endemic equilibrium P* is globally asymptotically stable when R0>1. Finally, some numerical simulations were presented to illustrate the analysis results.