In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

In the paper, the Linear–Quadratic–Gaussian (LQG) control strategy in regulatory mode (disturbance attenuation, zero value of the reference signal) in single-loop control is used to stabilize the system equipped in a non-integer order plant. The influence of the optimal controller design sophistication on control quality in terms of output variance is examined. It has been shown that the optimal implementation length of fractional-order difference is relatively low (several dozen in considered examples). Therefore, further increasing the controller’s complexity in terms of approximation length does not improve the control performance. Furthermore, it is presented that, under bounded control signal variance, the optimal fractional order of the controller may be significantly different from the actual fractional order of the plant (in the examples, the difference is up to 0.66).