Dynamical Analysis of a Delayed SIQS Epidemic Model on Scale-free Networks

In this paper, we establish a novel delayed SIQS epidemic model on scale-free networks, where time delay represents the average quarantine period. Through mathematical analysis, we present the basic reproduction number $R_{0}$. Then, we provide the global asymptotical stability of the disease-free equilibrium and the local asymptotical stability of the endemic equilibrium. Finally, we perform numerical simulations to verify the correctness of the main results and analyze the sensitivity of parameters. Our research shows that when $R_0>1$, lengthening the quarantine period can slow the spread of the disease and reduce the number of infected individuals.