Fractional dynamic analysis and optimal control problem for an SEIQR model on complex networks

A fractional order susceptible-exposed-infected-quarantined-recovered model is established on the complex networks. We calculate a specific expression for the basic reproduction number R0, prove the existence and uniqueness with respect to the solution, and prove the Ulam-Hyers stability of the model. Using the Latin hypercube sampling-partial rank correlation coefficient method, the influence of parameters on the R0 is analyzed. Based on the results of the analysis, the optimal control of the model is investigated as the control variables with vaccination rate and quarantine rate applying Pontryagin's minimum principle. The effects of α, degree of nodes, and network size on the model dynamics are simulated separately by the prediction correction method.