Stability and bifurcation analysis of SIQR for the COVID-19 epidemic model with time delay.

Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results.

Mathematical modeling and dynamic analysis of SIQR model with delay for pandemic COVID-19.

On the basis of the SIQR epidemic model, we consider the impact of treatment time on the epidemic situation, and we present a differential equation model with time-delay according to the characteristics of COVID-19. Firstly, we analyze the existence and stability of the equilibria in the modified COVID-19 epidemic model. Secondly, we analyze the existence of Hopf bifurcation, and derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, we determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, we carry out numerical simulations to verify the correctness of theoretical analysis with actual parameters, and show conclusions associated with the critical treatment time and the effect on epidemic for treatment time.